We analyze Age of Information (AoI) in wireless networks where nodes use a spatially adaptive random access scheme to send status updates to a central base station. We show that the set of achievable AoI in this setting is convex, and design policies to minimize weighted sum, min-max, and proportionally fair AoI by setting transmission probabilities as a function of node locations. We show that under the capture model, when the spatial topology of the network is considered, AoI can be significantly improved, and we obtain tight performance bounds on weighted sum and min-max AoI. Finally, we design a policy where each node sets its transmission probability based only on its own distance from the base station, when it does not know the positions of other nodes. We show that this policy achieves an AoI for all nodes within a factor of 2 from the optimal, and that it converges to the optimal proportionally fair policy as the size of the network goes to infinity.

We propose a framework for resource provisioning with QoS guarantees in shared infrastructure networks. Our novel framework provides tunable probabilistic service guarantees for throughput and delay. Key to our approach is a Modified Dirft-plus-Penalty (MDP) policy that ensures long-term stability while capturing short-term probabilistic service guarantees using linearized upper-confidence bounds. We characterize the feasible region of service guarantees and show that our MDP procedure achieves mean rate stability and an optimality gap that vanishes with the frame size over which service guarantees are provided. Finally empirical simulations validate our theory and demonstrate the favorable performance of our algorithm in handling QoS in multi-infrastructure networks.

We propose a novel Graph Neural Network (GNN) architecture and training framework for optimizing multi-class resource allocation in stochastic queueing networks. Our goal is to minimize metrics such as average delay, worst-case delay, and power consumption across diverse network topologies, traffic patterns, and link characteristics. Traditional GNNs struggle to model inter-class dependencies while preserving permutation invariance—a key property for generalization. To address this, we introduce Multi-Axis GNNs (MA-GNNs), which augment message passing with structured, permutation-invariant information exchange across traffic classes at each node. This enables reasoning over both spatial and inter-class dependencies via matrix-valued node and edge features. We train MA-GNNs using a Network Performance Gradient Algorithm—a model-free reinforcement learning method that directly optimizes routing coefficients for both state-independent and state-dependent policies, without requiring expert supervision. Experiments on diverse multi-hop, multi-commodity routing environments demonstrate that MA-GNNs consistently outperform classical baselines such as shortest-path and backpressure routing, while generalizing effectively to unseen networks.

An important choice in the design of satellite networks is whether the routing decisions are made in a distributed manner onboard the satellite, or centrally on a ground-based controller. We study the tradeoff between centralized and distributed routing in large-scale satellite networks. In particular, we consider a centralized routing scheme that has access to global but delayed network state information and a distributed routing scheme that has access to local but real-time network state information. For both routing schemes, we analyze the throughput and delay performance of shortest-path algorithms in networks with and without buffers onboard the satellites. We show that distributed routing outperforms centralized routing when the rate of change of the network link states is comparable to the inherent propagation and transmission rate. In particular, we show that in highly dynamic networks without buffers, the distributed scheme achieves higher throughput than a centralized scheme. In networks with buffers, the distributed scheme achieves lower delays for the same throughput.

Deep Reinforcement Learning (DRL) has become a powerful tool for developing control policies in queueing networks, but the common use of Multi-layer Perceptron (MLP) neural networks in these applications has significant drawbacks. MLP architectures, while versatile, often suffer from poor sample efficiency and a tendency to overfit training environments, leading to suboptimal performance on new, unseen networks. In response to these issues, we introduce a switch-type neural network (STN) architecture designed to improve the efficiency and generalization of DRL policies in queueing networks. The STN leverages structural patterns from traditional non-learning policies, ensuring consistent action choices across similar states. This design not only streamlines the learning process but also fosters better generalization by reducing the tendency to overfit. Our work presents three key contributions: first, the development of the STN as a more effective alternative to MLPs; second, empirical evidence showing that STNs achieve superior sample efficiency in various training scenarios; and third, experimental results demonstrating that STNs match MLP performance in familiar environments and significantly outperform them in new settings. By embedding domain-specific knowledge, the STN enhances the Proximal Policy Optimization (PPO) algorithm's effectiveness without compromising performance, suggesting its suitability for a wide range of queueing network control problems.

We study the design of scheduling policies to minimize the monitoring error of a collection of correlated sources, where only one source can be observed at any given time. We model correlated sources as a discrete-time Wiener process, where the increments are multivariate normal random variables, with a general covariance matrix that captures the correlation structure between the sources. Under a Kalman filter-based optimal estimation framework, we show that the performance of all scheduling policies oblivious to instantaneous error can be lower and upper bounded by the weighted sum of Age of Information (AoI) across the sources for appropriately chosen weights. We use this insight to design scheduling policies that are only a constant factor away from optimality, and make the rather surprising observation that AoI-based scheduling that ignores correlation is sufficient to obtain performance guarantees. We also derive scaling results showing that the optimal error scales roughly as the square of the system's dimensionality, even with correlation. Finally, we provide simulation results to verify our claims.

We propose Distributed Universal Max-Weight (DUMW) as a novel optimal control framework for distributed wireless SDN. DUMW is theoretically throughput-optimal and practically congruent with SDN system idiosyncrasies. Our algorithmic development non-trivially extends the throughput-optimal Universal Max-Weight (UMW) policy to permit distributed control and optimal inter-domain scheduling under the setting of heterogeneously delayed network state information. Furthermore, we design controller synchronization strategies that resolve the problem of multi-domain flow installation and are tailored to DUMW for maintaining throughput-optimality with negligible communication overhead. Extensive experiments validate our theoretical finding and demonstrate the favorable performance of DUMW. Under the setting of reliable links with wireless interference, DUMW achieves the same throughput as that of an optimal centralized controller and exhibits superiorscalability.

We study the design of scheduling policies to minimize monitoring error for a collection of correlated sources, where only one source can be observed at any given time. We model correlated sources as a discrete-time Wiener process, where the increments are multivariate normal random variables, with a general covariance matrix that captures the correlation structure between the sources. Under a Kalman filter based optimal estimation framework, we show that the performance of all scheduling policies oblivious to instantaneous error, can be lower and upper bounded by the weighted sum of Age of Information (AoI) across the sources for appropriately chosen weights. We use this insight to design scheduling policies that are only a constant factor away from optimality, and make the rather surprising observation that AoI-based scheduling that ignores correlation is sufficient to obtain performance guarantees. We also derive scaling results that show that the optimal error scales roughly as the square of the dimensionality of the system, even in the presence of correlation. Finally, we provide simulation results to verify our claims.

We analyze the problem of scheduling in wireless networks to meet end-to-end service guarantees. Using network slicing to decouple the queueing dynamics between flows, we show that the network's ability to meet hard throughput and deadline requirements is largely influenced by the scheduling policy. We characterize the feasible throughput/deadline region for a flow under a fixed route and set of slices, and find throughput- and deadline-optimal policies for a solitary flow. We formulate the feasibility problem for multiple flows in a general topology, and show its equivalence to finding a bounded-cost cycle on an exponentially large graph, which is un-solvable in polynomial time by the best-known algorithm. Using a novel concept called delay deficit, we develop a sufficient condition for meeting deadlines as a function of inter-scheduling times, and show that regular schedules are optimal for satisfying this condition. Motivated by this, we design a polynomial-time algorithm that returns an (almost) regular schedule, optimized to meet service guarantees for all flows.

Deep Reinforcement Learning (DRL) offers a powerful approach to training neural network control policies for stochastic queuing networks (SQN). However, traditional DRL methods rely on offline simulations or static datasets, limiting their real-world application in SQN control. This work proposes Online Deep Reinforcement Learning-based Controls (ODRLC) as an alternative, where an intelligent agent interacts directly with a real environment and learns an optimal control policy from these online interactions. SQNs present a challenge for ODRLC due to the unbounded nature of the queues within the network resulting in an unbounded state-space. An unbounded state-space is particularly challenging for neural network policies as neural networks are notoriously poor at extrapolating to unseen states. To address this challenge, we propose an intervention-assisted framework that leverages strategic interventions from known stable policies to ensure the queue sizes remain bounded. This framework combines the learning power of neural networks with the guaranteed stability of classical control policies for SQNs. We introduce a method to design these intervention-assisted policies to ensure strong stability of the network. Furthermore, we extend foundational DRL theorems for intervention-assisted policies and develop two practical algorithms specifically for ODRLC of SQNs. Finally, we demonstrate through experiments that our proposed algorithms outperform both classical control approaches and prior ODRLC algorithms.

Stochastic network models with all components being observable and controllable have been the focus of classic network optimization theory for decades. However, in modern network systems, it is common that the network controller can only observe and operate on some nodes (i.e., overlay nodes), and the other nodes (i.e., underlay nodes) are neither observable nor controllable. Moreover, the dynamics can be non-stochastic or even adversarial. In this paper, we focus on the network utility maximization (NUM) problem for networks with overlay-underlay structures. The network dynamics, such as packet admissions, external arrivals and control actions of underlay nodes, can be stochastic, non-stochastic or even adversarial. We propose the Tracking Drift-plus-Penalty (TDP*) algorithm that only operates on the overlay nodes and does not require direct observations of the underlay nodes, and analyze the tradeoffs between the average utility and queue backlog. We show that as long as the peak queue backlog of the network is sublinear in time horizon, TDP* can solve the NUM problem, i.e., reaching the maximum utility while preserving stability.

We develop a simple model for the timely monitoring of correlated sources over a wireless network. Using this model, we study how to optimize weighted-sum average Age of Information (AoI) in the presence of correlation. First, we discuss how to find optimal stationary randomized policies and show that they are at-most a factor of two away from optimal policies in general. Then, we develop a Lyapunov drift-based max-weight policy that performs better than randomized policies in practice and show that it is also at-most a factor of two away from optimal. Next, we derive scaling results that show how AoI improves in large networks in the presence of correlation. We also show that for stationary randomized policies, the expression for average AoI is robust to the way in which the correlation structure is modeled. Finally, for the setting where correlation parameters are unknown and time-varying, we develop a heuristic policy that adapts its scheduling decisions by learning the correlation parameters in an online manner. We also provide numerical simulations to support our theoretical results.

We consider a setting where multiple active sources send real-time updates over a single-hop wireless broadcast network to a monitoring station. Our goal is to design a scheduling policy that minimizes the time-average of general non-decreasing cost functions of Age of Information. We use a Whittle index based approach to find low complexity scheduling policies that have good performance. We prove that for a system with two sources, having possibly different cost functions and reliable channels, the Whittle index policy is exactly optimal. We derive structural properties of an optimal policy, that suggest that the performance of the Whittle index policy may be close to optimal in general. These results might also be of independent interest in the study of restless multi-armed bandit problems with similar underlying structure. We further establish that minimizing monitoring error for linear time-invariant systems and symmetric Markov chains is equivalent to minimizing appropriately chosen monotone functions of Age of Information. Finally, we provide simulations comparing the Whittle index policy with optimal scheduling policies found using dynamic programming, which support our results.

We consider the minimum delay routing problem in stochastic queueing networks where the goal is to find the optimal static routing policy that minimizes the average delay in the network. Previous works on minimum delay routing rely on knowledge of the delay function that maps the routing policies to their corresponding average delay, which is typically unavailable in stochastic queueing networks due to the complex dependency of the delay function on the distributional characteristics of network links. In this paper, we propose a learning approach to the minimum delay routing problem, whereby instead of relying on aprior information on the delay function, we seek to learn the delay function through observations. We design an algorithm that leverages finite-time observations of network queue lengths to approximate the values of the delay function, uses the approximate values to estimate the gradient of the delay function, and performs gradient descent based on the estimated gradient to optimize the routing policy. We prove that our algorithm converges to the optimal static routing policy when the delay function is convex, which is a reasonable condition in practical settings. We conduct extensive simulations to evaluate the empirical performance of our algorithm, demonstrating its superior delay performance over static policies and even dynamic policies such as Join-the-Shortest-Queue and BackPressure.

We consider a wireless network with a base station broadcasting and collecting time-sensitive data to and from spatially distributed nodes in the presence of wireless interference. The Age of Information (AoI) is the time that has elapsed since the most-recently delivered packet was generated, and captures the freshness of information. In the context of broadcast and collection, we define the Age of Broadcast (AoB) to be the amount of time elapsed until all nodes receive a fresh update, and the Age of Collection (AoC) as the amount of time that elapses until the base station receives an update from all nodes. We quantify the average broadcast and collection ages in two scenarios: 1) instance-dependent, in which the locations of all nodes and interferers are known, and 2) instance-independent, in which they are not known but are located randomly, and expected age is characterized with respect to node locations. In the instance-independent case, we show that AoB and AoC scale super-exponentially with respect to the radius of the region surrounding the base station. Simulation results highlight how expected AoB and AoC are affected by network parameters such as network density, medium access probability, and the size of the coverage region.

We consider the design of distributed scheduling algorithms that minimize age of information in single-hop wireless networks. The centralized max-weight policy is known to be nearly optimal in this setting; hence, our goal is to design a distributed CSMA scheme that can mimic its performance. To that end, we propose a distributed protocol called Fresh-CSMA and show that in an idealized setting, Fresh-CSMA can match the scheduling decisions of the max-weight policy with high probability in each frame, and also match the theoretical performance guarantees of the max-weight policy over the entire time horizon. We then consider a more realistic setting and study the impact of protocol parameters on the probability of collisions and the overhead caused by the distributed nature of the protocol. Finally, we provide simulations that support our theoretical results and show that the performance gap between the ideal and realistic versions of Fresh-CSMA is small.

The emergence of large-scale wireless networks with partially-observable and time-varying dynamics has imposed new challenges on the design of optimal control policies. This paper studies efficient scheduling algorithms for wireless networks subject to generalized interference constraint, where mean arrival and mean service rates are unknown and non-stationary. This model exemplifies realistic edge devices' characteristics of wireless communication in modern networks. We propose a novel algorithm termed MW-UCB for generalized wireless network scheduling, which is based on the Max-Weight policy and leverages the Sliding-Window Upper-Confidence Bound to learn the channels' statistics under non-stationarity. MW-UCB is provably throughput-optimal under mild assumptions on the variability of mean service rates. Specifically, as long as the total variation in mean service rates over any time period grows sub-linearly in time, we show that MW-UCB can achieve the stability region arbitrarily close to the stability region of the class of policies with full knowledge of the channel statistics. Extensive simulations validate our theoretical results and demonstrate the favorable performance of MW-UCB.

We consider the optimal routing problem in a discrete-time system with a job dispatcher connected to$M$parallel servers. At every time slot, the job dispatcher sends the incoming jobs to a server for execution, with each server having a queue that stores the jobs. The arrival process of incoming jobs, and the service processes of the servers are stochastic with unknown and possibly heterogeneous rates. Each server$s_{m}$is associated with an underlying utility$v_{m}$that is initially unknown. Whenever server$s_{m}$completes a job, a utility of$v_{m}$is obtained and a noisy observation of$v_{m}$is received. The goal is to design a policy that makes routing decisions to maximize the total utility obtained by the end of a finite time horizon$T$. The performance of policies is measured in terms of regret, which is the additive difference between the expected total utility obtained by the policy and the supremum of the expected total utility over all the policies. The optimal routing problem can be interpreted as a problem of multi-armed bandit with queues where each server is viewed as an arm and the completion of a job is viewed as a pull of an arm. The key distinction between the optimal routing problem and traditional multi-armed bandit problems is in the queueing dynamics at the server, which arises due to the stochastic nature of the arrival and service processes. Our results combine techniques from control of stochastic queueing systems and stochastic multi-armed bandits to provide insights to the design and analysis of policies for the optimal routing problem. We first present analytical bounds that link the regret to the utilization and queue length of servers. Next, we start by assuming that the ordering of the underlying utilities is known and introduce the Priority-$K$routing policy which makes priority-based routing decisions that send the incoming jobs to the server of the highest underlying utility with queue length no larger than a threshold$K$. We prove that Priority-$K$achieves$O(\log T)$-regret with an appropriately chosen$K$. Next, removing the assumption of known utility ordering, we propose the Upper-Confidence Priority-$K$policy, which essentially combines the Priority-$K$policy with the ordering based on the upper-confidence bounds of the underlying utilities, and establish that the Upper-Confidence Priority-$K$policy achieves an instance-dependent$O(\log ^{3} T)$-regret. Finally, we extend our results to the a generalized version of the optimal routing problem with multiple job dispatchers in a bipartite network. Our theoretical results are also validated by simulations.

Modern networks are complex and may include components that cannot be fully controlled or observed. Such network models can be characterized by overlay-underlay structures, where the network controller can only observe and operate on overlay nodes, and the underlay nodes are neither observable nor controllable. Classic network control algorithms may fail to work properly if they are only applied to the overlay nodes. To tackle this issue, we propose the Tracking MaxWeight (TMW*) algorithm that does not require direct observations of underlay nodes and only operates on overlay nodes. TMW* maintains virtual queues that track the dynamics of the underlay nodes and makes control decisions based on those virtual queues. We show that TMW* is throughput optimal as long as the network is stabilizable. We further extend our analysis to the setting that the estimates of the underlay state is erroneous and show that as long as the errors scale sub-linearly in time, TMW* preserves throughput optimality.

We consider the problem of minimizing age of information in multihop wireless networks and propose three classes of policies to solve the problem - stationary randomized, age difference, and age debt. For the unicast setting with fixed routes between each source-destination pair, we first develop a procedure to find age optimal Stationary Randomized policies. These policies are easy to implement and allow us to derive closed-form expression for average AoI. Next, for the same unicast setting, we develop a class of heuristic policies, called Age Difference, based on the idea that if neighboring nodes try to reduce their age differential then all nodes will have fresher updates. This approach is useful in practice since it relies only on the local age differential between nodes to make scheduling decisions. Finally, we propose the class of policies called Age Debt, which can handle 1) non-linear AoI cost functions; 2) unicast, multicast and broadcast flows; and 3) no fixed routes specified per flow beforehand. Here, we convert AoI optimization problems into equivalent network stability problems and use Lyapunov drift to find scheduling and routing schemes that stabilize the network. We also provide numerical results comparing our proposed classes of policies with the best known scheduling and routing schemes available in the literature for a wide variety of network settings.

Consider a stream learning system with a source and a set of computation nodes that solves a machine learning task modeled as stochastic convex optimization problem over an unknown distribution D. The source generates i.i.d. data points from D and routes the data points to the computation nodes for processing. The data points are processed in a streaming fashion, i.e., each data point can be accessed only once and is discarded after processing. The system employs local stochastic gradient descent (local SGD), where each computation node performs stochastic gradient descent locally using the data it receives from the source and periodically synchronizes with other computation nodes. Since the routing policy of the source determines the availability of data points at each computation node, the performance of the system, i.e., the optimization error obtained by local SGD, depends on the routing policy.In this paper, we study the influence of the routing policy on the performance of stream learning systems. We first derive an upper bound on the optimization error as a function of the routing policy. The upper bound reveals that the routing policy influences the performance through tuning the bias-variance trade-off of the optimization process, and gives rise to a framework for optimizing the routing policy for stream learning systems. By minimizing the upper bound, we propose an optimal static routing policy that achieves the best trade-off for stream learning systems with deterministic data generation process. We then propose a routing policy that can approximate the optimal static routing policy arbitrarily closely for systems where the data points are generated according to a stochastic process with unknown rate. Finally, we conduct simulations using Support Vector Machine as the machine learning task on a real data set, and show that the optimal static routing policy has excellent empirical performance in terms of minimizing the optimization error and the proposed stochastic routing policy closely matches the optimal static routing policy.

We develop a simple model for the timely monitoring of correlated sources over a wireless network. Using this model, we study how to optimize weighted-sum average Age of Information (AoI) in the presence of correlation. First, we discuss how to find optimal stationary randomized policies and show that they are at-most a factor of two away from optimal policies in general. Then, we develop a Lyapunov drift-based max-weight policy that performs better than randomized policies in practice and show that it is also at-most a factor of two away from optimal. Next, we derive scaling results that show how AoI improves in large networks in the presence of correlation. We also show that for stationary randomized policies, the expression for average AoI is robust to the way in which the correlation structure is modeled. Finally, for the setting where correlation parameters are unknown and time-varying, we develop a heuristic policy that adapts its scheduling decisions by learning the correlation parameters in an online manner. We also provide numerical simulations to support our theoretical results.

Network Utility Maximization (NUM) studies the problems of allocating traffic rates to network users in order to maximize the users’ total utility subject to network resource constraints. In this paper, we propose a new NUM framework, Learning-NUM, where the users’ utility functions are unknown apriori and the utility function values of the traffic rates can be observed only after the corresponding traffic is delivered to the destination, which means that the utility feedback experiences queueing delay. The goal is to design a policy that gradually learns the utility functions and makes rate allocation and network scheduling/routing decisions so as to maximize the total utility obtained over a finite time horizon$T$. In addition to unknown utility functions and stochastic constraints, a central challenge of our problem lies in the queueing delay of the observations, which may be unbounded and depends on the decisions of the policy. We first show that the expected total utility obtained by the best dynamic policy is upper bounded by the solution to a static optimization problem. Without the presence of feedback delay, we design an algorithm based on the ideas of gradient estimation and Max-Weight scheduling. To handle the feedback delay, we embed the algorithm in a parallel-instance paradigm to form a policy that achieves$\tilde {O}(T^{3/4})$-regret, i.e., the difference between the expected utility obtained by the best dynamic policy and our policy is in$\tilde {O}(T^{3/4})$. Furthermore, we extend our policy to deal with the case where the utility observations are noisy and show that it achieves$\tilde {O}(T^{7/8})$-regret. Finally, to demonstrate the practical applicability of the Learning-NUM framework, we apply it to three application scenarios including database query, job scheduling and video streaming. We further conduct simulations on the job scheduling application to evaluate the empirical performance of our policy.

Emerging applications, such as smart factories and fleets of drones, increasingly rely on sharing time-sensitive information for monitoring and control. In such application domains, it is essential to keep information fresh, as outdated information loses its value and can lead to system failures and safety risks. The Age-of-Information is a performance metric that captures how fresh the information is from the perspective of the destination.In this paper, we show that as the congestion in the wireless network increases, the Age-of-Information degrades sharply, leading to outdated information at the destination. Leveraging years of theoretical research, we propose WiFresh: an unconventional architecture that achieves near optimal information freshness in wireless networks of any size, even when the network is overloaded. Our experimental results show that WiFresh can improve information freshness by two orders of magnitude when compared to an equivalent standard WiFi network. We propose and realize two strategies for implementing WiFresh: one at the MAC layer using hardware-level programming and another at the Application layer using Python.

We consider a Random Access network with a number of nodes transmitting time-sensitive information to a wireless base station. Packets are generated according to a stochastic process and nodes employ either Slotted-ALOHA or Carrier-Sense Multiple Access (CSMA) to transmit these packets. A packet collision occurs when two or more nodes transmit simultaneously and a successful packet transmission occurs when a node transmits without interference. The goal is to optimize the Random Access mechanism in terms of information freshness, which is captured by the Age of Information (AoI) metric.In this paper, we propose a framework to analyze and optimize the average AoI in Random Access networks with stochastic packet generation. In particular, we develop a discrete-time model, derive an approximate expression for the average AoI in the network, and then use this expression to optimize the Random Access mechanism. Furthermore, we implement the optimized Random Access mechanism in a Software Defined Radio testbed and compare the AoI measurements with analytical and numerical results in order to validate our framework. Our approach allows us to evaluate the combined impact of the packet generation rate, transmission probability, and size of the network on the AoI performance.

Network Utility Maximization (NUM) studies the problems of allocating traffic rates to network users in order to maximize the users' total utility subject to network resource constraints. In this paper, we propose a new NUM framework, Learning-NUM, where the users' utility functions are unknown apriori and the utility function values of the traffic rates can be observed only after the corresponding traffic is delivered to the destination, which means that the utility feedback experiences queueing delay. The goal is to design a policy that gradually learns the utility functions and makes rate allocation and network scheduling/routing decisions so as to maximize the total utility obtained over a finite time horizon T. In addition to unknown utility functions and stochastic constraints, a central challenge of our problem lies in the queueing delay of the observations, which may be unbounded and depends on the decisions of the policy. We first show that the expected total utility obtained by the best dynamic policy is upper bounded by the solution to a static optimization problem. Without the presence of feedback delay, we design an algorithm based on the ideas of gradient estimation and Max-Weight scheduling. To handle the feedback delay, we embed the algorithm in a parallel-instance paradigm to form a policy that achieves Õ(T3/4)-regret, i.e., the difference between the expected utility obtained by the best dynamic policy and our policy is in Õ(T3/4). Finally, to demonstrate the practical applicability of the Learning-NUM framework, we apply it to three application scenarios including database query, job scheduling and video streaming. We further conduct simulations on the job scheduling application to evaluate the empirical performance of our policy.

We consider systems that require timely monitoring of sources over a communication network, where the cost of delayed information is unknown, time-varying and possibly adversarial. For the single source monitoring problem, we design algorithms that achieve sublinear regret compared to the best fixed policy in hindsight. For the multiple source scheduling problem, we design a new online learning algorithm called Follow the Perturbed Whittle Leader and show that it has low regret compared to the best fixed scheduling policy in hindsight, while remaining computationally feasible. The algorithm and its regret analysis are novel and of independent interest to the study of online restless multi-armed bandit problems. We further design algorithms that achieve sublinear regret compared to the best dynamic policy when the environment is slowly varying. Finally, we apply our algorithms to a mobility tracking problem. We consider non-stationary and adversarial mobility models and illustrate the performance benefit of using our online learning algorithms compared to an oblivious scheduling policy.

We consider a single-hop wireless network with sources transmitting time-sensitive information to the destination over multiple unreliable channels. Packets from each source are generated according to a stochastic process with known statistics and the state of each wireless channel (ON/OFF) varies according to a stochastic process with unknown statistics. The reliability of the wireless channels is to be learned through observation. At every time-slot, the learning algorithm selects a single pair (source, channel) and the selected source attempts to transmit its packet via the selected channel. The probability of a successful transmission to the destination depends on the reliability of the selected channel. The goal of the learning algorithm is to minimize the Age-of-Information (AoI) in the network over T time-slots. To analyze its performance, we introduce the notion of AoI-regret, which is the difference between the expected cumulative AoI of the learning algorithm under consideration and the expected cumulative AoI of a genie algorithm that knows the reliability of the channels a priori. The AoI-regret captures the penalty incurred by having to learn the statistics of the channels over the T time-slots. The results are two-fold: first, we consider learning algorithms that employ well-known solutions to the stochastic multi-armed bandit problem (such as ϵ-Greedy, Upper Confidence Bound, and Thompson Sampling) and show that their AoI-regret scales as Θ(log T); second, we develop a novel learning algorithm and show that it has O(1) regret. To the best of our knowledge, this is the first learning algorithm with bounded AoI-regret.

We investigate the problem of co-designing computation and communication in a multi-agent system (e.g., a sensor network or a multi-robot team). We consider the realistic setting where each agent acquires sensor data and is capable of local processing before sending updates to a base station, which is in charge of making decisions or monitoring phenomena of interest in real time. Longer processing at an agent leads to more informative updates but also larger delays, giving rise to a delay-accuracy trade-off in choosing the right amount of local processing at each agent. We assume that the available communication resources are limited due to interference, bandwidth, and power constraints. Thus, a scheduling policy needs to be designed to suitably share the communication channel among the agents. To that end, we develop a general formulation to jointly optimize the local processing at the agents and the scheduling of transmissions. Our novel formulation leverages the notion of Age of Information to quantify the freshness of data and capture the delays caused by computation and communication. We develop efficient resource allocation algorithms using the Whittle index approach and demonstrate our proposed algorithms in two practical applications: multi-agent occupancy grid mapping in time-varying environments, and ride sharing in autonomous vehicle networks. Our experiments show that the proposed codesign approach leads to a substantial performance improvement (18 – 82% in our tests).

We summarize recent contributions in the broad area of age of information (AoI). In particular, we describe the current state of the art in the design and optimization of low-latency cyberphysical systems and applications in which sources send time-stamped status updates to interested recipients. These applications desire status updates at the recipients to be as timely as possible; however, this is typically constrained by limited system resources. We describe AoI timeliness metrics and present general methods of AoI evaluation analysis that are applicable to a wide variety of sources and systems. Starting from elementary single-server queues, we apply these AoI methods to a range of increasingly complex systems, including energy harvesting sensors transmitting over noisy channels, parallel server systems, queueing networks, and various single-hop and multi-hop wireless networks. We also explore how update age is related to MMSE methods of sampling, estimation and control of stochastic processes. The paper concludes with a review of efforts to employ age optimization in cyberphysical applications.

We consider a system consisting of a single transmitter/receiver pair and N channels over which they may communicate. Packets randomly arrive to the transmitter's queue and wait to be successfully sent to the receiver. The transmitter may attempt a frame transmission on one channel at a time, where each frame includes a packet if one is in the queue. For each channel, an attempted transmission is successful with an unknown probability. The transmitter's objective is to quickly identify the best channel to minimize the number of packets in the queue over T time slots. To analyze system performance, we introduce queue length regret, which is the expected difference between the total queue length of a learning policy and a controller that knows the rates, a priori. One approach to designing a transmission policy would be to apply algorithms from the literature that solve the closely-related stochastic multi-armed bandit problem. These policies would focus on maximizing the number of successful frame transmissions over time. However, we show that these methods have Ω(log T) queue length regret. On the other hand, we show that there exists a set of queue-length based policies that can obtain order optimal O(1) queue length regret. We use our theoretical analysis to devise heuristic methods that are shown to perform well in simulation.

We consider an m server system in which each server can service at most one update packet at a time. The system designer controls (1) scheduling - the order in which the packets get serviced, (2) routing - the server that an arriving update packet joins for service, and (3) the service time distribution with fixed service rate. Given a fixed update generation process, we prove a strong age-delay and age-delay variance tradeoff, wherein, as the average AoI approaches its minimum, the packet delay and its variance approach infinity. In order to prove this result, we consider two special cases of the m server system, namely, a single server system with last come first served with preemptive service and an infinite server system. In both these cases, we derive sufficient conditions to show that three heavy tailed service time distributions, namely Pareto, log-normal, and Weibull, asymptotically minimize the average AoI as their tail gets heavier, and establish the age-delay tradeoff results. We provide an intuitive explanation as to why such a seemingly counter intuitive age-delay tradeoff is natural, and that it should exist in many systems.

We consider a wireless network with a base station serving multiple traffic streams to different destinations. Packets from each stream arrive to the base station according to a stochastic process and are enqueued in a separate (per stream) queue. The queueing discipline controls which packet within each queue is available for transmission. The base station decides, at every time t, which stream to serve to the corresponding destination. The goal of scheduling decisions is to keep the information at the destinations fresh. Information freshness is captured by the Age of Information (AoI) metric. In this paper, we derive a lower bound on the AoI performance achievable by any given network operating under any queueing discipline. Then, we consider three common queueing disciplines and develop both an Optimal Stationary Randomized policy and a Max-Weight policy under each discipline. Our approach allows us to evaluate the combined impact of the stochastic arrivals, queueing discipline and scheduling policy on AoI. We evaluate the AoI performance both analytically and using simulations. Numerical results show that the performance of the Max-Weight policy is close to the analytical lower bound.

We consider the problem of efficient packet dissemination in wireless networks with point-to-multipoint wireless broadcast channels. We propose a dynamic policy, which achieves the broadcast capacity of the network. This policy is obtained by first transforming the original multi-hop network into a precedence-relaxed virtual single-hop network and then finding an optimal broadcasting policy for the relaxed network. The resulting policy is shown to be throughput-optimal for the original wireless network using a sample-path argument. We also prove the NP-completeness of the finite-horizon broadcasting problem, which is in contrast with the polynomial-time solvability of the problem with point-to-point channels. Illustrative simulation results demonstrate the efficacy of the proposed broadcast policy in achieving the full broadcast capacity with low delay.

Distributed computing networks, tasked with both packet transmission and processing, require the joint optimization of communication and computation resources. We develop a dynamic control policy that determines both routes and processing locations for packets upon their arrival at a distributed computing network. The proposed policy, referred to as Universal Computing Network Control (UCNC), guarantees that packets i) are processed by a specified chain of service functions, ii) follow cycle-free routes between consecutive functions, and iii) are delivered to their corresponding set of destinations via proper packet duplications. UCNC is shown to be throughput-optimal for any mix of unicast and multicast traffic, and is the first throughput-optimal policy for non-unicast traffic in distributed computing networks with both communication and computation constraints. Moreover, simulation results suggest that UCNC yields substantially lower average packet delay compared with existing control policies for unicast traffic.

Emerging applications, such as smart factories and fleets of drones, increasingly rely on sharing time-sensitive information for monitoring and control. In such application domains, it is essential to keep information fresh, as outdated information loses its value and can lead to system failures and safety risks. The Age of Information (AoI) is a performance metric that captures how fresh the information is from the perspective of the destination. In this paper, we show that as the congestion in the wireless network increases, the AoI degrades sharply, leading to outdated information at the destination. Leveraging years of theoretical research, we propose and implement WiFresh: an unconventional architecture that achieves near optimal information freshness in wireless networks, regardless of the level of congestion. Our experimental results show that WiFresh can improve information freshness by two orders of magnitude when compared to an equivalent standard WiFi network.

Age of information is a new network performance metric that captures the freshness of information at end-users. This paper studies the age of information from a scheduling perspective. To that end, we consider a wireless broadcast network where a base-station (BS) is updating many users on random information arrivals under a transmission capacity constraint. For the offline case when the arrival statistics are known to the BS, we develop a structural MDP scheduling algorithm and an index scheduling algorithm, leveraging Markov decision process (MDP) techniques and the Whittle's methodology for restless bandits. By exploring optimal structural results, we not only reduce the computational complexity of the MDP-based algorithm, but also simplify deriving a closed form of the Whittle index. Moreover, for the online case, we develop an MDP-based online scheduling algorithm and an index-based online scheduling algorithm. Both the structural MDP scheduling algorithm and the MDP-based online scheduling algorithm asymptotically minimize the average age, while the index scheduling algorithm minimizes the average age when the information arrival rates for all users are the same. Finally, the algorithms are validated via extensive numerical studies.

Futuristic communication network formed by autonomously operated, unmanned aerial vehicles, has piqued researchers interests in highly mobile wireless networks. Exchanging safety critical information, with low latency and high throughput, in such systems is of paramount importance. We study the broadcast capacity and minimum delay scaling laws for such highly mobile wireless networks, in which each node has to disseminate packets to all other nodes in the network. In particular, we consider a cell partitioned network under an IID mobility model, in which each node chooses a new position at random, every time slot. We derive scaling laws for broadcast capacity and minimum delay as a function of the network size. We propose a simple first-come-first-serve flooding scheme, which nearly achieve both capacity and minimum delay scaling. Thus, in contrast to what has been speculated in the literature, we show that there is nearly no tradeoff between capacity and delay. Our results also show that high mobility does not improve broadcast capacity. Our analysis makes use of the theory of Markov Evolving Graphs (MEGs), and develops two new bounds on flooding time in MEGs by relaxing the previously required expander property assumption. Simulation results verify our analysis, and throw up interesting open problems.

Throughput-optimal transmission scheduling in wireless networks has been a well considered problem in the literature, and the method for achieving optimality, MaxWeight scheduling, has been known for several decades. This algorithm achieves optimality by adaptively scheduling transmissions relative to each user's stochastic traffic demands. To implement the method, users must report their queue backlogs to the network controller and must rapidly respond to the resulting resource allocations. However, many currently-deployed wireless systems are not able to perform these tasks and instead expect to occupy a fixed assignment of resources. To accommodate these limitations, adaptive scheduling algorithms need to interactively estimate these uncooperative users' queue backlogs and make scheduling decisions to account for their predicted behavior. In this work, we address the problem of scheduling with uncooperative legacy systems by developing algorithms to accomplish these tasks. We begin by formulating the problem of inferring the uncooperative systems' queue backlogs as a partially observable Markov decision process and proceed to show how our resulting learning algorithms can be successfully used in a queue-length-based scheduling policy. Our theoretical analysis characterizes the throughput-stability region of the network and is verified using simulation results.

Age of information (AoI) is a recently proposed metric for measuring information freshness. AoI measures the time that elapsed since the last received update was generated. We consider the problem of minimizing average and peak AoI in a wireless networks, consisting of a set of source-destination links, under general interference constraints. When fresh information is always available for transmission, we show that a stationary scheduling policy is peak age optimal. We also prove that this policy achieves average age that is within a factor of two of the optimal average age. In the case where fresh information is not always available, and packet/information generation rate has to be controlled along with scheduling links for transmission, we prove an important separation principle: the optimal scheduling policy can be designed assuming fresh information, and independently, the packet generation rate control can be done by ignoring interference. Peak and average AoI for discrete time G/Ber/1 queue is analyzed for the first time, which may be of independent interest.

Age of information (AoI), defined as the time that elapsed since the last received update was generated, is a newly proposed metric to measure the timeliness of information updates in a network. We consider AoI minimization problem for a network with general interference constraints, and time varying channels. We propose two policies, namely, virtual-queue based policy and age-based policy when the channel state is available to the network scheduler at each time step. We prove that the virtual-queue based policy is nearly optimal, up to a constant additive factor, and the age-based policy is at-most a factor of 4 away from optimality. Comparison with previous work, which derived age optimal policies when channel state information is not available to the scheduler, demonstrates significant improvement in age due to the availability of channel state information. Our analysis relies on the age conservation law and age-square conservation law developed in this paper, which hold more generally and may be of independent interest.

Massive data centers are at the heart of the Internet. The rapid growth of Internet traffic and the abundance of rich data-driven applications have raised the need for enormous network bandwidth. Towards meeting this growing traffic demand, optical interconnects have gained significant attention, as they can provide high throughput, low latency, and scalability. In particular, optical Wavelength Division Multiplexing (WDM) provides the possibility to build data centers comprising of millions of servers, while providing hundreds of terabits per second bandwidth. In this paper, we propose a WDM-based Reconfigurable Hierarchical Optical Data Center Architecture (RHODA) that can satisfy future Internet traffic demands. To improve scalability, our DCN architecture is hierarchical, as it groups server racks into clusters. Cluster membership is reconfigurable through the use of optical switches. Each cluster enables heavy-traffic communication among the racks within. To support varying traffic patterns, the inter-cluster network topology and link capacities are also reconfigurable, which is achieved through the use of optical space switches and Wavelength Selective Switches (WSSs). Our simulation results demonstrate that in terms of average hop distance, RHODA outperforms OSA, FatTree and WaveCube by up to 81%, 66% and 60%, respectively.

Traditional network interdiction refers to the problem of an interdictor trying to reduce the throughput of network users by removing network edges. In this paper, we propose a new paradigm for network interdiction that models scenarios, such as stealth DoS attack, where the interdiction is performed through injecting adversarial traffic flows. Under this paradigm, we first study the deterministic flow interdiction problem, where the interdictor has perfect knowledge of the operation of network users. We show that the problem is highly inapproximable on general networks and is NP-hard even when the network is acyclic. We then propose an algorithm that achieves a logarithmic approximation ratio and quasi-polynomial time complexity for acyclic networks through harnessing the submodularity of the problem. Next, we investigate the robust flow interdiction problem, which adopts the robust optimization framework to capture the case where definitive knowledge of the operation of network users is not available. We design an approximation framework that integrates the aforementioned algorithm, yielding a quasi-polynomial time procedure with poly-logarithmic approximation ratio for the more challenging robust flow interdiction. Finally, we evaluate the performance of the proposed algorithms through simulations, showing that they can be efficiently implemented and yield near-optimal solutions.

The effectiveness of many optimal network control algorithms (e.g., BackPressure) relies on the premise that all of the nodes are fully controllable. However, these algorithms may yield poor performance in a partially-controllable network where a subset of nodes are uncontrollable and use some unknown policy. Such a partially-controllable model is of increasing importance in real-world networked systems such as overlay-underlay networks. In this paper, we design optimal network control algorithms that can stabilize a partially-controllable network. We first study the scenario where uncontrollable nodes use a queue-agnostic policy, and propose a low-complexity throughput-optimal algorithm, called Tracking-MaxWeight (TMW), which enhances the original MaxWeight algorithm with an explicit learning of the policy used by uncontrollable nodes. Next, we investigate the scenario where uncontrollable nodes use a queue-dependent policy and the problem is formulated as an MDP with unknown queueing dynamics. We propose a new reinforcement learning algorithm, called Truncated Upper Confidence Reinforcement Learning (TUCRL), and prove that TUCRL achieves tunable three-way tradeoffs between throughput, delay and convergence rate.

We consider the problem of timely exchange of updates between a central station and a set of ground terminals$V$, via a mobile agent that traverses across the ground terminals along a mobility graph$G = (V, E)$. We design the trajectory of the mobile agent to minimize average-peak and average age of information (AoI), two recently proposed metrics for measuring timeliness of information. We consider randomized trajectories, in which the mobile agent travels from terminal$i$to terminal$j$with probability$P_{i,j}$. For the information gathering problem, we show that a randomized trajectory is average-peak age optimal and factor-$8\mathcal {H}$average age optimal, where$\mathcal {H}$is the mixing time of the randomized trajectory on the mobility graph$G$. We also show that the average age minimization problem is NP-hard. For the information dissemination problem, we prove that the same randomized trajectory is factor-$O(\mathcal {H})$average-peak and average age optimal. Moreover, we propose an age-based trajectory, which utilizes information about current age at terminals, and show that it is factor-2 average age optimal in a symmetric setting.

Age-of-information (AoI) is a newly proposed performance metric of information freshness. It differs from the traditional delay metric, because it is destination centric and measures the time that elapsed since the last received fresh information update was generated at the source. We show that AoI and packet delay differ in a fundamental way in certain systems, i.e. minimizing one can imply maximizing the other. We consider two queueing systems, namely a single server last come first serve queue with preemptive service (LCFSp) and G/G/∞ queue, and show that a heavy tailed service distribution, that results in the worst case packet delay or variance in packet delay, respectively, minimizes AoI. For the specific case of M/G/1 LCFSp and G/G/∞ queue, we also prove that deterministic service, that minimizes packet delay and variance in packet delay, respectively, results in the worst case AoI.

Information freshness and low latency communication is important to many emerging applications. While Age of Information (AoI) serves as a metric of information freshness, packet delay is a traditional metric of communication latency. We prove that there is a natural tradeoff between the AoI and packet delay. We consider a single server system, in which at most one update packet can be serviced at a time. The system designer controls the order in which the packets get serviced and the service time distribution, with a given service rate. We analyze two tradeoff problems that minimize packet delay and the variance in packet delay, respectively, subject to an average age constraint. We prove a strong age-delay and age-delay variance tradeoff, wherein, as the average age approaches its minimum, the delay and its variance approach infinity. We show that the service time distribution that minimizes average age, must necessarily have an unbounded-second moment.

We consider a wireless network with a base station serving multiple traffic streams to different destinations. Packets from each stream arrive to the base station according to a stochastic process and are enqueued in a separate (per stream) queue. The queueing discipline controls which packet within each queue is available for transmission. The base station decides, at every time t, which stream to serve to the corresponding destination. The goal of scheduling decisions is to keep the information at the destinations fresh. Information freshness is captured by the Age of Information (AoI) metric.

We consider the problem of inferring the topology of a network using the measurements available at the end nodes, without cooperation from the internal nodes. To this end, we provide a simple method to obtain path interference which identifies whether two paths in the network intersect with each other. Using this information, we formulate the topology inference problem as an integer program and develop polynomial time algorithms to solve it optimally for networks with tree and ring topologies. Finally, we use the insight developed from these algorithms to develop a heuristic for identifying general topologies. Simulation results show that our heuristic outperforms a recently proposed algorithm that uses distance measurements for topology discovery.

We address the problem of optimal routing in overlay networks. An overlay network is constructed by adding new overlay nodes on top of a legacy network. The overlay nodes are capable of implementing any dynamic routing policy, however, the legacy underlay has a fixed, single path routing scheme and uses a simple work-conserving forwarding policy. Moreover, the underlay routes are pre-determined and unknown to the overlay network. The overlay network can increase the achievable throughput of the legacy network by using multiple routes, which consist of direct routes and indirect routes through other overlay nodes. We develop an optimal dynamic routing algorithm for such overlay networks called the Optimal Overlay Routing Policy (OORP). OORP is derived using the classical dual subgradient descent method, and it can be implemented in a distributed manner. We show that the queue-lengths can be used as a substitute for the dual variables in the algorithm. However, the underlay queue-lengths are unknown to the overlay, so we propose two regression based schemes that learn simplified models of the backlog in the underlay using historical data and use them to estimate the queue-lengths in real time. Simulation results show that near-optimal performance can be achieved without any knowledge of the underlay.

While the current generation of mobile and fixed communication networks has been standardized for mobile broadband services, the next generation is driven by the vision of the Internet of Things and mission-critical communication services requiring latency in the order of milliseconds or submilliseconds. However, these new stringent requirements have a large technical impact on the design of all layers of the communication protocol stack. The cross-layer interactions are complex due to the multiple design principles and technologies that contribute to the layers' design and fundamental performance limitations. We will be able to develop low-latency networks only if we address the problem of these complex interactions from the new point of view of submilliseconds latency. In this paper, we propose a holistic analysis and classification of the main design principles and enabling technologies that will make it possible to deploy low-latency wireless communication networks. We argue that these design principles and enabling technologies must be carefully orchestrated to meet the stringent requirements and to manage the inherent tradeoffs between low latency and traditional performance metrics. We also review currently ongoing standardization activities in prominent standards associations, and discuss open problems for future research.

In spectrum-sharing networks, primary users have the right to preempt secondary users, which can significantly degrade the performance of underlying secondary users. In this paper, we use backup channels to provide reliability guarantees for secondary users. In particular, we study the optimal white channel assignment that minimizes the amount of recovery capacity (i.e., bandwidth of backup channels) needed to meet a given reliability guarantee, where both deterministic and probabilistic requirements are considered. This problem is shown to be coupled by two NP-hard objectives. We characterize the structure of the optimal assignment and develop bi-criteria approximation algorithms. Moreover, we investigate the scaling of the recovery capacity as the network size becomes large. It is shown that the recovery capacity is negligible as compared to the total traffic demands in a large-scale network.

We consider the problem of throughput-optimal broadcasting in time-varying wireless network with an underlying Directed Acyclic Graph (DAG) topology. Known broadcast algorithms route packets along pre-computed spanning trees. In large wireless networks with time-varying connectivities, the optimal trees are difficult to compute and maintain. In this paper we propose a new online throughput-optimal broadcast algorithm, which takes packet-by-packet scheduling and routing decisions, obviating the need for maintaining any global topological structures, such as spanning-trees. Our algorithm utilizes certain queue-like system-state information for making transmission decisions and hence, may be thought of as a generalization of the well-known back pressure algorithm, which makes point-to-point unicast transmission decisions based on local queue-length information. Technically, the back-pressure algorithm is derived by stabilizing the packet-queues. However, because of packet-duplications, the work-conservation principle is violated and appropriate queuing processes are difficult to define in the broadcast setting. To address this fundamental issue, we identify certain state-variables whose dynamics behave like virtual queues. By stochastically stabilizing these virtual queues, we devise a throughput-optimal broadcast policy. We also derive new characterizations of the broadcast-capacity of time-varying wireless DAGs and derive an efficient algorithm to compute the capacity exactly under certain assumptions, and a poly-time approximation algorithm for computing the capacity approximately under less restrictive assumptions.

Age of Information (AoI) is a performance metric that captures the freshness of the information from the perspective of the destination. The AoI measures the time that elapsed since the generation of the packet that was most recently delivered to the destination. In this paper, we consider a single-hop wireless network with a number of nodes transmitting time-sensitive information to a base station and address the problem of minimizing the expected weighted sum AoI of the network while simultaneously satisfying timely-throughput constraints from the nodes. We develop four low-complexity transmission scheduling policies that attempt to minimize AoI subject to minimum throughput requirements and evaluate their performance against the optimal policy. In particular, we develop a randomized policy, a Max-Weight policy, a Drift-Plus-Penalty policy, and a Whittle's Index policy, and show that they are guaranteed to be within a factor of two, four, two, and eight, respectively, away from the minimum AoI possible. The simulation results show that Max-Weight and Drift-Plus-Penalty outperform the other policies, both in terms of AoI and throughput, in every network configuration simulated, and achieve near-optimal performance.

Age of Information (AoI) is a performance metric that captures the freshness of the information from the perspective of the destination. The AoI measures the time that elapsed since the generation of the packet that was most recently delivered to the destination. In this paper, we consider a single-hop wireless network with a number of nodes transmitting time-sensitive information to a Base Station and address the problem of minimizing the Expected Weighted Sum AoI of the network while simultaneously satisfying timely-throughput constraints from the nodes. We develop three low-complexity transmission scheduling policies that attempt to minimize AoI subject to minimum throughput requirements and evaluate their performance against the optimal policy. In particular, we develop a randomized policy, a Max-Weight policy and a Whittle's Index policy, and show that they are guaranteed to be within a factor of two, four and eight, respectively, away from the minimum AoI possible. In contrast, simulation results show that Max-Weight outperforms the other policies, both in terms of AoI and throughput, in every network configuration simulated, and achieves near optimal performance.

Stochastic models have been dominant in network optimization theory for over two decades, due to their analytical tractability. However, these models fail to capture non-stationary or even adversarial network dynamics which are of increasing importance for modeling the behavior of networks under malicious attacks or characterizing short-term transient behavior. In this paper, we consider the network utility maximization problem in adversarial network settings. In particular, we focus on the tradeoffs between total queue length and utility regret which measures the difference in network utility between a causal policy and an “oracle” that knows the future within a finite time horizon. Two adversarial network models are developed to characterize the adversary's behavior. We provide lower bounds on the tradeoff between utility regret and queue length under these adversarial models, and analyze the performance of two control policies (i.e., the Drift-plus-Penalty algorithm and the Tracking Algorithm).

Distributed computing networks, tasked with both packet transmission and processing, require the joint optimization of communication and computation resources. We develop a dynamic control policy that determines both routes and processing locations for packets upon their arrival at a distributed computing network. The proposed policy, referred to as Universal Computing Network Control (UCNC), guarantees that packets i) are processed by a specified chain of service functions, ii) follow cycle-free routes between consecutive functions, and iii) are delivered to their corresponding set of destinations via proper packet duplications. UCNC is shown to be throughput-optimal for any mix of unicast and multicast traffic, and is the first throughput-optimal policy for non-unicast traffic in distributed computing networks with both communication and computation constraints. Moreover, simulation results suggest that UCNC yields substantially lower average packet delay compared with existing control policies for unicast traffic.

We consider a system consisting of a single transmitter and N channels. Packets randomly arrive to the transmitter's queue, and at each time slot a controller can schedule one of the N channels for transmission. The channel's rates are time-varying with unknown statistics and must be learned through observation. Our objective is to minimize the number of packets in the system's queue over T time slots. We define the regret of the system to be the expected difference between the total queue length of a controller that must learn the channels' average rates and a controller that knows the rates, a priori. One approach to solving this problem would be to apply algorithms from the literature that were developed to solve the closely-related stochastic multi-armed bandit problem. However, we show that these methods have Ω(log(T)) queue length regret. On the other hand, we show that there exists a set of queue-length based policies that are able to obtain order optimal, O(1), regret.

Age of information (AoI) is a recently proposed metric that measures the time elapsed since the generation of the last received information update. We consider the problem of AoI minimization for a network under general interference constraints, and time varying channel. We study the case where the channel statistics are known, but the current channel state is unknown. We propose two scheduling policies, namely, the virtual queue based policy and age-based policy. In the virtual queue based policy, the scheduler schedules links with maximum weighted sum of the virtual queue lengths, while in the age-based policy, the scheduler schedules links with maximum weighted sum of a function of link AoI. We prove that the virtual queue based policy is peak age optimal, up to an additive constant, while the age-based policy is at most factor 4 away from the optimal age. Numerical results suggest that both the proposed policies are, in fact, very close to the optimal.

We study the problem of learning channel statistics in order to efficiently schedule transmissions in wireless networks subject to interference constraints. In particular, we focus on the primary interference model which requires that at any time the set of activated links be a matching in the corresponding graph. We propose a distributable algorithm that forms greedy matchings in the graph in order to learn the channels' transmission rates, while simultaneously exploiting previous observations to obtain high throughput. Comparison to the offline solution shows our algorithm to have good performance that scales well with the number of links in the network. We then turn our attention to the stochastic setting where packets randomly arrive to the network and await transmission in queues at the nodes. We develop a queue-length-based scheduling policy that uses the channel learning algorithm as a component. We analyze our method in time varying environments and show that it achieves the same stability region as that of a greedy matching policy with full channel knowledge (i.e., half of the full stability region).

Complex systems such as smart cities and smart power grids rely heavily on their interdependent components. The failure of a component in one network may lead to the failure of the supported component in another network. Components which support a large number of interdependent components may be more vulnerable to attacks and failures. In this paper, we study the robustness of two interdependent networks under node failures. By modeling each network using a random geometric graph (RGG), we study conditions for the percolation of two interdependent RGGs after in-homogeneous node failures. We derive analytical bounds on the interdependent degree thresholds (k1,k2), such that the interdependent RGGs percolate after removing nodes in Githat support more than kjnodes in Gj(∀i, j ∈ {1, 2}, i ≠ j). We verify the bounds using numerical simulation, and show that there is a tradeoff between k1and k2for maintaining percolation after the failures.

We consider the Network Utility Maximization (NUM) problem for wireless networks in the presence of arbitrary types of flows, including unicast, broadcast, multicast, and anycast traffic. Building upon the recent framework of a universal control policy (UMW), we design a utility optimal cross-layer admission control, routing and scheduling policy, called UMW+. The UMW+ policy takes packet level actions based on a precedence-relaxed virtual network. Using Lyapunov optimization techniques, we show that UMW+ maximizes network utility, while simultaneously keeping the physical queues in the network stable. Extensive simulation results validate the performance of UMW+ demonstrating both optimal utility performance and bounded average queue occupancy. Moreover, we establish a precise one-to-one correspondence between the dynamics of the virtual queues under the UMW+ policy, and the dynamics of the dual variables of an associated offline NUM program, under a subgradient algorithm. This correspondence sheds further insight into our understanding of UMW+.

Age of information (AoI), defined as the time elapsed since the last received update was generated, is a newly proposed metric to measure the timeliness of information updates in a network. We consider AoI minimization problem for a network with general interference constraints, and time varying channels. We propose two policies, namely, virtual-queue based policy and age-based policy when the channel state is available to the network scheduler at each time step. We prove that the virtual-queue based policy is nearly optimal, up to a constant additive factor, and the age-based policy is at-most factor 4 away from optimality. Comparison with previous work, which derived age optimal policies when channel state information is not available to the scheduler, demonstrates a 4 fold improvement in age due to the availability of channel state information.

The performance of wireless scheduling algorithms directly depends on the availability and accuracy of channel state information (CSI) at the scheduler. As CSI updates must propagate across the network, they are delayed as they arrive at the controller. In this paper, we analyze the effect that delayed CSI has on the throughput performance of scheduling in wireless networks. By accounting for the delays in CSI as they relate to the network topology, we revisit the comparison between centralized and distributed scheduling. We explore the tradeoff between optimal centralized scheduling using delayed CSI and imperfect distributed scheduling using timely CSI. In particular, we show that under certain conditions distributed scheduling outperforms the optimal centralized scheduling policy and we characterize the point at which distributed scheduling outperforms centralized scheduling for tree and clique networks. Lastly, we propose a partially distributed scheme that achieves high throughput amidst delayed CSI.

In this paper, we consider a wireless broadcast network with a base station sending time-sensitive information to a number of clients through unreliable channels. The Age of Information (AoI), namely the amount of time that elapsed since the most recently delivered packet was generated, captures the freshness of the information. We formulate a discrete-time decision problem to find a transmission scheduling policy that minimizes the expected weighted sum AoI of the clients in the network. We first show that in symmetric networks, a greedy policy, which transmits the packet for the client with the highest current age, is optimal. For general networks, we develop three low-complexity scheduling policies: a randomized policy, a Max-Weight policy and a Whittle's Index policy, and derive performance guarantees as a function of the network configuration. To the best of our knowledge, this is the first work to derive performance guarantees for scheduling policies that attempt to minimize AoI in wireless networks with unreliable channels. Numerical results show that both the Max-Weight and Whittle's Index policies outperform the other scheduling policies in every configuration simulated, and achieve near optimal performance.

We consider the problem of throughput-optimal packet dissemination, in the presence of an arbitrary mix of unicast, broadcast, multicast, and anycast traffic, in an arbitrary wireless network. We propose an online dynamic policy, called Universal Max-Weight (UMW), which solves the problem efficiently. To the best of our knowledge, UMW is the first known throughput-optimal policy of such versatility in the context of generalized network flow problems. Conceptually, the UMW policy is derived by relaxing the precedence constraints associated with multi-hop routing and then solving a min-cost routing and max-weight scheduling problem on a virtual network of queues. When specialized to the unicast setting, the UMW policy yields a throughput-optimal cycle-free routing and link scheduling policy. This is in contrast with the well-known throughput-optimal back-pressure (BP) policy which allows for packet cycling, resulting in excessive latency. Extensive simulation results show that the proposed UMW policy incurs a substantially smaller delay as compared with the BP policy. The proof of throughput-optimality of the UMW policy combines ideas from the stochastic Lyapunov theory with a sample path argument from adversarial queueing theory and may be of independent theoretical interest.

In wireless communication networks, interference models are routinely used for tasks, such as performance analysis, optimization, and protocol design. These tasks are heavily affected by the accuracy and tractability of the interference models. Yet, quantifying the accuracy of these models remains a major challenge. In this paper, we propose a new index for assessing the accuracy of any interference model under any network scenario. Specifically, it is based on a new index that quantifies the ability of any interference model in correctly predicting harmful interference events, that is, link outages. We consider specific wireless scenario of both conventional sub-6 GHz and millimeter-wave networks and demonstrate how our index yields insights into the possibility of simplifying the set of dominant interferers, replacing a Nakagami or Rayleigh random fading by an equivalent deterministic channel, and ignoring antenna sidelobes. Our analysis reveals that in highly directional antenna settings with obstructions, even simple interference models (such as the classical protocol model) are accurate, while with omnidirectional antennas, more sophisticated and complex interference models (such as the classical physical model) are necessary. Our new approach makes it possible to adopt the simplest interference model of adequate accuracy for every wireless network.

A coflow is a collection of parallel flows belonging to the same job. It has the all-or-nothing property: a coflow is not complete until the completion of all its constituent flows. In this paper, we focus on optimizing coflow-level delay, i.e., the time to complete all the flows in a coflow, in the context of an N × N input-queued switch. In particular, we develop a throughput-optimal scheduling policy that achieves the best scaling of coflow-level delay as N → ∞. We first derive lower bounds on the coflow-level delay that can be achieved by any scheduling policy. It is observed that these lower bounds critically depend on the variability of flow sizes. Then we analyze the coflow-level performance of some existing coflow-agnostic scheduling policies and show that none of them achieves provably optimal performance with respect to coflow-level delay. Finally, we propose the Coflow-Aware Batching (CAB) policy which achieves the optimal scaling of coflow-level delay under some mild assumptions.

We consider the problem of throughput-optimal packet dissemination, in the presence of an arbitrary mix of unicast, broadcast, multicast and anycast traffic, in a general wireless network. We propose an online dynamic policy, called Universal Max-Weight (UMW), which solves the above problem efficiently. To the best of our knowledge, UMW is the first throughput-optimal algorithm of such versatility in the context of generalized network flow problems. Conceptually, the UMW policy is derived by relaxing the precedence constraints associated with multi-hop routing, and then solving a min-cost routing and max-weight scheduling problem on a virtual network of queues. When specialized to the unicast setting, the UMW policy yields a throughput-optimal cycle-free routing and link scheduling policy. This is in contrast to the well-known throughput-optimal BackPressure (BP) policy which allows for packet cycling, resulting in excessive delay. Extensive simulation results show that the proposed policy incurs a substantially lower delay as compared to the BP policy. The proof of throughput-optimality of the UMW policy combines techniques from stochastic Lyapunov theory with a sample path argument from adversarial queueing theory and may be of independent theoretical interest.

We consider a model of two interdependent networks, where every node in one network depends on one or more supply nodes in the other network and a node fails if it loses all of its supply nodes. We develop algorithms to compute the failure probability of a path, and obtain the most reliable path between a pair of nodes in a network, under the condition that each supply node fails independently with a given probability. Our work generalizes the classical shared risk group model, by considering multiple risks associated with a node and letting a node fail if all the risks occur. Moreover, we study the diverse routing problem by considering two paths between a pair of nodes. We define two paths to be d-failure resilient if at least one path survives after removing d or fewer supply nodes, which generalizes the concept of disjoint paths in a single network, and risk-disjoint paths in a classical shared risk group model. We compute the probability that both paths fail, and develop algorithms to compute the most reliable pair of paths.

Age of information is a newly proposed metric that captures delay from an application layer perspective. The age measures the amount of time that elapsed from the moment the mostly recently received update was generated until the present time. In this paper, we study an age minimization problem over a wireless broadcast network with many users, where only one user can be served at a time. We formulate a Markov decision process (MDP) to find dynamic transmission scheduling schemes, with the purpose of minimizing the long-run average age. While showing that an optimal scheduling algorithm for the MDP is a simple stationary switch-type, we propose a sequence of finite-state approximations for our infinite-state MDP and prove its convergence. We then propose both optimal off-line and online scheduling algorithms for the finite-approximate MDPs, depending on knowledge of time-varying arrivals.

We consider the problem of efficient packet dissemination in wireless networks with point-to-multi-point wireless broadcast channels. We propose a dynamic policy, which achieves the broadcast capacity of the network. This policy is obtained by first transforming the original multi-hop network into a precedence-relaxed virtual single-hop network and then finding an optimal broadcast policy for the relaxed network. The resulting policy is shown to be throughput-optimal for the original wireless network using a sample-path argument. We also prove the NP-completeness of the finite-horizon broadcast problem, which is in contrast with the polynomial time solvability of the problem with point-to-point channels. Illustrative simulation results demonstrate the efficacy of the proposed broadcast policy in achieving the full broadcast capacity with low delay.

We study broadcast capacity and minimum delay scaling laws for highly mobile wireless networks, in which each node has to disseminate or broadcast packets to all other nodes in the network. In particular, we consider a cell partitioned network under the simplified independent and identically distributed (IID) mobility model, in which each node chooses a new cell at random every time slot. We derive scaling laws for broadcast capacity and minimum delay as a function of the cell size. We propose a simple first-come-first-serve (FCFS) flooding scheme that nearly achieves both capacity and minimum delay scaling. Our results show that high mobility does not improve broadcast capacity, and that both capacity and delay improve with increasing cell sizes. In contrast to what has been speculated in the literature we show that there is (nearly) no tradeoff between capacity and delay. Our analysis makes use of the theory of Markov Evolving Graphs (MEGs) and develops two new bounds on flooding time in MEGs by relaxing the previously required expander property assumption.

We consider a multi-channel communication system in which a transmitter has access to M channels, but does not know the state of any of the channels. We model the channel state using an ON/OFF Markov process, and allow the transmitter to probe a single channel at predetermined probing intervals to decide over which channel to transmit. For models in which the transmitter must transmit over the probed channel, it has been shown that a myopic policy probing the channel most likely to be ON is optimal. In this paper, we allow the transmitter to select a channel over which to transmit that is potentially different from the probed channel. For a system of two channels, we show that the choice of which channel to probe does not affect the throughput. For a system with many channels, we show that a probing policy that probes the channel that is the second-most likely to be ON results in higher throughput. We extend the channel probing problem to dynamically choose when to probe based on probing history, and characterize the optimal probing policy for various scenarios.

We consider the problem of providing protection against failures in wireless networks subject to interference constraints. Typically, protection in wired networks is provided through the provisioning of dedicated backup paths. This approach has not been previously considered in the wireless setting due to the prohibitive cost of backup capacity. Assigning capacity for dedicated backup paths in a wireless setting can more than double the total resources required from what was needed without protection, which can make protection infeasible. However, we show that in the presence of interference, guaranteed protection can be provided for all demands with little, and oftentimes no , additional resources beyond what was required without any protection. This is due to the fact that after a failure, links that previously interfered with the failed link can be activated, thus leading to a “recapturing” of lost capacity. We provide an ILP formulation to find an optimal solution for both binary and SINR interference constraints, and develop corresponding time-efficient algorithms. Our approach utilizes up to 87 percent less protection resources than traditional disjoint path routing to provide guaranteed protection. For the case of 2-hop interference, our protection scheme requires only 8 percent more resources on average than providing no protection whatsoever.

Time-varying graphs are a useful model for networks with dynamic connectivity such as vehicular networks, yet, despite their great modeling power, many important features of time-varying graphs are still poorly understood. In this paper, we study the survivability properties of time-varying networks against unpredictable interruptions. We first show that the traditional definition of survivability is not effective in time-varying networks, and propose a new survivability framework. To evaluate the survivability of time-varying networks under the new framework, we propose two metrics that are analogous to MaxFlow and MinCut in static networks. We show that some fundamental survivability-related results such as Menger's Theorem only conditionally hold in time-varying networks. Then, we analyze the complexity of computing the proposed metrics and develop approximation algorithms. Finally, we conduct trace-driven simulations to demonstrate the application of our survivability framework in the robust design of a real-world bus communication network.

We consider the impact of delayed state information on the performance of centralized wireless scheduling algorithms. Since state updates must be collected from throughout the network, they are inevitably delayed, and this delay is proportional to the distance of each respective node to the controller. In this paper, we analyze the optimal controller placement resulting from this delayed state information. We propose a dynamic controller placement framework, in which the controller is relocated using delayed queue length information at each node, and transmissions are scheduled based on channel and queue length information. We characterize the throughput region under such policies, and find a policy that stabilizes the system for all arrival rates within the throughput region.

Legacy networks are often designed to operate with simple single-path routing, like the shortest path, which is known to be throughput suboptimal. On the other hand, previously proposed throughput optimal policies (i.e., backpressure) require every device in the network to make dynamic routing decisions. In this paper, we study an overlay architecture for dynamic routing, such that only a subset of devices (overlay nodes) need to make the dynamic routing decisions. We determine the essential collection of nodes that must bifurcate traffic for achieving the maximum multi-commodity network throughput. We apply our optimal node placement algorithm to several graphs and the results show that a small fraction of overlay nodes is sufficient for achieving maximum throughput. Finally, we propose a threshold-based policy (BP-T) and a heuristic policy (OBP), which dynamically control traffic bifurcations at overlay nodes. Policy BP-T is proved to maximize throughput for the case when underlay paths do no overlap. In all studied simulation scenarios, OBP not only achieves full throughput but also reduces delay in comparison to the throughput optimal backpressure routing.

The backpressure routing policy is known to be a throughput optimal policy that supports any feasible traffic demand, but may have poor delay performance when packets traverse loops in the network. In this paper, we study loop-free backpressure routing policies that forward packets along directed acyclic graphs (DAGs) to avoid the looping problem. These policies use link reversal algorithms to improve the DAGs in order to support any achievable traffic demand. For a network with a single commodity, we show that a DAG that supports a given traffic demand can be found after a finite number of iterations of the link-reversal process. We use this to develop a joint link-reversal and backpressure routing policy, called the loop free backpressure (LFBP) algorithm. This algorithm forwards packets on the DAG, while the DAG is dynamically updated based on the growth of the queue backlogs. We show by simulations that such a DAG-based policy improves the delay over the classical backpressure routing policy. We also propose a multicommodity version of the LFBP algorithm and via simulation show that its delay performance is better than that of backpressure.

We study the problem of efficiently disseminating packets in multi-hop wireless networks. At each time slot, the network controller activates a set of non-interfering links and forward selected copies of packets on each activated link. The maximum rate of commonly received packets is referred to as the broadcast capacity of the network. Existing policies achieve the broadcast capacity by balancing traffic over a set of spanning trees, which are difficult to maintain in a large and time-varying wireless network. In this paper, we propose a new dynamic algorithm that achieves the broadcast capacity when the underlying network topology is a directed acyclic graph (DAG). This algorithm is decentralized, utilizes local information only, and does not require the use of spanning trees. The principal methodological challenge inherent in this problem is the absence of work-conservation principle due to the duplication of packets, which renders usual queuing modeling inapplicable. We overcome this difficulty by studying relative packet deficits and imposing in-order delivery constraints to every node in the network. We show that in-order delivery is throughput-optimal in DAGs and can be exploited to simplify the design and analysis of optimal algorithms. Our capacity characterization also leads to a polynomial time algorithm for computing the broadcast capacity of any wireless DAG under the primary interference constraints. In addition, we propose a multiclass extension of our algorithm, which can be effectively used for broadcasting in any network with arbitrary topology. Simulation results show that the our algorithm has a superior delay performance as compared with the traditional tree-based approaches.

In this paper we design throughput-optimal dynamic broadcast algorithms for multi-hop networks with arbitrary topologies. Most of the previous broadcast algorithms route packets along spanning trees, rooted at the source node. For large time-varying networks, computing and maintaining a set of spanning trees is not efficient, as the network-topology may change frequently. In this paper we design a class of dynamic algorithms which make packet-by-packet scheduling and routing decisions and hence, obviate the need for maintaining any global topological structures, such as spanning trees. Our algorithms may be conveniently understood as a non-trivial generalization of the familiar back-pressure algorithm, which makes unicast packet routing and scheduling decisions, based on local queue-length information and does not require to maintain end-to-end paths. However, in the broadcast setting, due to packet duplications, it is hard to define appropriate queuing structures. We design and prove the optimality of a virtual-queue based algorithm, where virtual-queues are defined for subsets of nodes. We then propose a multi-class broadcast policy which combines the above scheduling algorithm with in-class-in-order packet forwarding, resulting in significant reduction in complexity. Finally, we evaluate performance of the proposed algorithms via extensive numerical simulations.

We consider shielding critical links to enhance the robustness of a network, in which shielded links are resilient to failures. We first study the problem of increasing network connectivity by shielding links that belong to small cuts of a network, which improves the network reliability under random link failures. We then focus on the problem of shielding links to guarantee network connectivity under geographical and general failure models. We develop a mixed integer linear program (MILP) to obtain the minimum cost shielding to guarantee the connectivity of a single source-destination pair under a general failure model, and exploit geometric properties to decompose the shielding problem under a geographical failure model. We extend our MILP formulation to guarantee the connectivity of the entire network, and use Benders decomposition to significantly reduce the running time. We also apply simulated annealing to obtain near-optimal solutions in much shorter time. Finally, we extend the algorithms to guarantee partial network connectivity, and observe significant reduction in the shielding cost, especially when the geographical failure region is small.

We develop a new framework for measuring and comparing the accuracy of any wireless interference models used in the analysis and design of wireless networks. Our approach is based on a new index that assesses the ability of the interference model to correctly predict harmful interference events, i.e., link outages. We use this new index to quantify the accuracy of various interference models used in the literature, under various scenarios such as Rayleigh fading wireless channels, directional antennas, and blockage (impenetrable obstacles) in the network. Our analysis reveals that in highly directional antenna settings with obstructions, even simple interference models (e.g., the classical protocol model) are accurate, while with omnidirectional antennas, more sophisticated and complex interference models (e.g., the classical physical model) are necessary. Our new approach makes it possible to adopt the appropriate interference model of adequate accuracy and simplicity in different settings.

Time-varying graphs are a useful model for networks with dynamic connectivity such as vehicular networks, yet, despite their great modeling power, many important features of time-varying graphs are still poorly understood. In this paper, we study the survivability properties of time-varying networks against unpredictable interruptions. We first show that the traditional definition of survivability is not effective in time-varying networks, and propose a new survivability framework. To evaluate the survivability of time-varying networks under the new framework, we propose two metrics that are analogous to MaxFlow and MinCut in static networks. We show that some fundamental survivability-related results such as Menger's Theorem only conditionally hold in time-varying networks. Then we analyze the complexity of computing the proposed metrics and develop approximation algorithms. Finally, we conduct trace-driven simulations to demonstrate the application of our survivability framework in the robust design of a real-world bus communication network.

We consider an opportunistic communication system in which a secondary transmitter communicates over the unused time slots of a primary user. In particular, we consider a system in which the primary user is uncooperative and transmits whenever its buffer is nonempty, and the secondary user relies on feedback from its receiver in order to decide when to transmit. The objective of the secondary user is to maximize its own throughput without degrading the throughput of the primary user. We analyze the maximum achievable throughput of the secondary user by formulating the problem as a partially observable Markov decision process. We derive bounds on the optimal solution and find a channel access policy for the secondary user that is near-optimal when the primary user's exogenous arrival rate is low. These results are then used to characterize the set of arrival rates to the primary and secondary users that may be stably supported by the system.

In spectrum-sharing networks, primary users have the right to preempt secondary users, which significantly degrades the performance of underlying secondary users. In this paper, we use backup channels to provide reliability guarantees for secondary users. In particular, we study the optimal white channel assignment that minimizes the amount of recovery capacity (i.e., bandwidth of backup channels) needed to meet a given reliability guarantee. This problem is shown to be coupled by two NP-hard objectives. We characterize the structure of the optimal assignment and develop bi-criteria approximation algorithms. Moreover, we investigate the scaling of the recovery capacity as the network size becomes large. It is shown that the recovery capacity is negligible as compared to the total traffic demands in a large-scale network.

In order to steer antenna beams towards one another for communication, wireless nodes with highly-directional antennas must track the channel state of their neighbors. To keep this overhead manageable, each node must limit the number of neighbors that it tracks. The subset of neighbors that each node chooses to track constitutes a network topology over which traffic can be routed. We consider this topology design problem, taking into account channel modeling, transmission scheduling, and traffic demand. We formulate the optimal topology design problem, with the objective of maximizing the scaling of traffic demand, and propose a distributed method, where each node rapidly builds a segment of the topology around itself by forming connections with its nearest neighbors in discretized angular regions. The method has low complexity and message passing overhead. The resulting topologies are shown to have desirable structural properties and approach the optimal solution in high path loss environments.

In this work, we explore the performance of backpressure routing and scheduling for TCP flows over wireless networks. TCP and backpressure are not compatible due to a mismatch between the congestion control mechanism of TCP and the queue size based routing and scheduling of the backpressure framework. We propose a TCP-aware backpressure routing and scheduling mechanism that takes into account the behavior of TCP flows. TCP-aware backpressure provides throughput optimality guarantees in the Lyapunov optimization framework, and gracefully combines TCP and backpressure without making any changes to the TCP protocol. The simulation results show that TCP-aware backpressure (i) improves the throughput of TCP flows significantly, (ii) provides fairness across competing TCP flows, and (iii) accommodates both TCP and non-TCP flows in a wireless network, and improves throughput of these flows without hurting fairness.

We study multihop networks with flow-scheduling constraints, no constraints on simultaneous activation of different links, potentially multiple source-destination routes, and a mix of heavy-tailed and light-tailed traffic. In this setting, we analyze the delay performance of the widely studied class of Back-Pressure scheduling policies, known for their throughput optimality property, using as a performance criterion the notion of delay stability, i.e., whether the expected end-to-end delay in steady state is finite. Our analysis highlights the significance of “bottleneck links,” i.e., links that are allowed to serve the source queues of heavy-tailed flows. The main idea is that traffic that has to pass through bottleneck links experiences large delays under Back-Pressure. By means of simple examples, we provide insights into how the network topology, the routing constraints, and the link capacities may facilitate or hinder the ability of light-tailed flows to avoid bottlenecks. Our delay-stability analysis is greatly simplified by the use of fluid approximations, allowing us to derive analytical results that would have been hard to obtain through purely stochastic arguments. Finally, we show how to achieve the best performance with respect to the delay stability criterion, by using a parameterized version of the Back-Pressure policy.

We present a novel control scheme that dynamically optimizes multirate multicast. By computing the differential backlog at every node, our scheme adaptively allocates transmission rates per session/user pair in order to maximize throughput. An important feature of the proposed scheme is that it does not require source cooperation or centralized calculations. This methodology leads to efficient and distributed algorithms that scale gracefully and can be embraced by low-cost wireless devices. Additionally, it is shown that maximization of sum utility is possible by the addition of a virtual queue at each destination node of the multicast groups. The virtual queue captures the desire of the individual user and helps in making the correct resource allocation to optimize total utility. Under the operation of the proposed schemes backlog sizes are deterministically bounded, which provides delay guarantees on delivered packets. To illustrate its practicality, we present a prototype implementation in the NITOS wireless testbed. The experimental results verify that the proposed schemes achieve maximum performance while maintaining low complexity.

Backpressure routing and scheduling, with its throughput-optimal operation guarantee, is a promising technique to improve throughput in wireless multihop networks. Although backpressure is conceptually viewed as layered, the decisions of routing and scheduling are made jointly, which imposes several challenges in practice. In this work, we present Diff-Max, an approach that separates routing and scheduling and has three strengths: 1) Diff-Max improves throughput significantly; 2) the separation of routing and scheduling makes practical implementation easier by minimizing cross-layer operations; i.e., routing is implemented in the network layer and scheduling is implemented in the link layer; and 3) the separation of routing and scheduling leads to modularity; i.e., routing and scheduling are independent modules in Diff-Max, and one can continue to operate even if the other does not. Our approach is grounded in a network utility maximization (NUM) formulation and its solution. Based on the structure of Diff-Max, we propose two practical schemes: Diff-subMax and wDiff-subMax. We demonstrate the benefits of our schemes through simulation in ns-2.

We study the problem of broadcasting packets in wireless networks. At each time slot, a network controller activates non-interfering links and forwards packets to all nodes at a common rate; the maximum rate is referred to as the broadcast capacity of the wireless network. Existing policies achieve the broadcast capacity by balancing traffic over a set of spanning trees, which are difficult to maintain in a large and time-varying wireless network. We propose a new dynamic algorithm that achieves the broadcast capacity when the underlying network topology is a directed acyclic graph (DAG). This algorithm utilizes local queue-length information, does not use any global topological structures such as spanning trees, and uses the idea of in-order packet delivery to all network nodes. Although the in-order packet delivery constraint leads to degraded throughput in cyclic graphs, we show that it is throughput optimal in DAGs and can be exploited to simplify the design and analysis of optimal algorithms. Our simulation results show that the proposed algorithm has superior delay performance as compared to tree-based approaches.

We consider the age-of-information in a multi-class M/G/1 queueing system, where each class generates packets containing status information. Age of information is a relatively new metric that measures the amount of time that elapsed between status updates, thus accounting for both the queueing delay and the delay between packet generation. This gives rise to a tradeoff between frequency of status updates, and queueing delay. In this paper, we study this tradeoff in a system with heterogenous users modeled as a multi-class M/G/1 queue. To this end, we derive the exact peak age-of-Information (PAoI) profile of the system, which measures the “freshness” of the status information. We then seek to optimize the age of information, by formulating the problem using quasiconvex optimization, and obtain structural properties of the optimal solution.

We consider the problem of scheduling transmissions over a wireless downlink when channel state information (CSI) is not available to the transmitter. We assume channel states are time varying and evolve according to a Markov Chain. We show that using current QLI does not stabilize the system due to correlations between backlog and channel state. We show that the throughput optimal scheduling policy in this context must use delayed queue length information (QLI). We characterize the extent to which QLI must be delayed as a function of the channel state statistics.

The performance of wireless scheduling algorithms directly depends on the availability and accuracy of channel state information (CSI) at the scheduler. As CSI updates must propagate across the network, they are delayed as they arrive at the controller. In this paper, we analyze the effect that delayed CSI has on the throughput performance of scheduling in wireless networks. By accounting for the delays in CSI as they relate to the network topology, we revisit the comparison between centralized and distributed scheduling, which is analyzed as a trade-off between using delayed CSI and making imperfect scheduling decisions. In particular, we prove that there exist conditions under which distributed scheduling outperforms the optimal centralized scheduling policy. We characterize the point at which distributed scheduling outperforms centralized scheduling for tree networks, illustrating the impact of topology on throughput.

The backpressure routing policy is known to be a throughput optimal policy that supports any feasible traffic demand in data networks, but may have poor delay performance when packets traverse loops in the network. In this paper, we study loop-free backpressure routing policies that forward packets along directed acyclic graphs (DAGs) to avoid the looping problem. These policies use link reversal algorithms to improve the DAGs in order to support any achievable traffic demand.

The performance of wireless scheduling algorithms directly depends on the availability and accuracy of network state information at the scheduler. As channel state updates must propagate across the network, they are delayed as they arrive at the controller. The location of the controller directly affects the attainable throughput, as its dictates the delays with which information is obtained to make scheduling decisions. In this paper, we analyze the optimal controller placement over a network in which CSI delays are proportional to distance. We propose a dynamic controller placement framework, in which the controller is relocated using delayed queue length information at each node, and scheduling is done using delayed QLI and CSI. We characterize the throughput region under such policies, and find a policy which stabilizes the system for all arrival rates within the throughput region.

We consider the optimal control problem for networks subjected to time-varying channels, reconfiguration delays, and interference constraints. We show that the simultaneous presence of time-varying channels and reconfiguration delays significantly reduces the system stability region and changes the structure of optimal policies. We first consider memoryless channel processes and characterize the stability region in closed form. We prove that a frame-based Max-Weight scheduling algorithm that sets frame durations dynamically, as a function of the current queue lengths and average channel gains, is throughput-optimal. Next, we consider arbitrary Markov-modulated channel processes and show that memory in the channel processes can be exploited to improve the stability region. We develop a novel approach to characterizing the stability region of such systems using state-action frequencies, which are stationary solutions to a Markov Decision Process (MDP) formulation. Moreover, we develop a dynamic control policy using the state-action frequencies and variable frames whose lengths are functions of queue sizes and show that it is throughput-optimal. The frame-based dynamic control (FBDC) policy is applicable to a broad class of network control systems, with or without reconfiguration delays, and provides a new framework for developing throughput-optimal network control policies using state-action frequencies. Finally, we propose Myopic policies that are easy to implement and have better delay properties as compared to the FBDC policy.

This paper presents a scheme in which a dedicated backup network is designed to provide protection from random link failures. Upon a link failure in the primary network, traffic is rerouted through a preplanned path in the backup network. We introduce a novel approach for dealing with random link failures, in which probabilistic survivability guarantees are provided to limit capacity over provisioning. We show that the optimal backup routing strategy in this respect depends on the reliability of the primary network. Specifically, as primary links become less likely to fail, the optimal backup networks employ more resource sharing among backup paths. We apply results from the field of robust optimization to formulate an ILP for the design and capacity provisioning of these backup networks. We then propose a simulated annealing heuristic to solve this problem for large-scale networks and present simulation results that verify our analysis and approach.

We consider utility maximization in networks where the sources do not employ flow control and may consequently overload the network. In the absence of flow control at the sources, some packets will inevitably have to be dropped when the network is in overload. To that end, we first develop a distributed, threshold-based packet-dropping policy that maximizes the weighted sum throughput. Next, we consider utility maximization and develop a receiver-based flow control scheme that, when combined with threshold-based packet dropping, achieves the optimal utility. The flow control scheme creates virtual queues at the receivers as a push-back mechanism to optimize the amount of data delivered to the destinations via back-pressure routing. A new feature of our scheme is that a utility function can be assigned to a collection of flows, generalizing the traditional approach of optimizing per-flow utilities. Our control policies use finite-buffer queues and are independent of arrival statistics. Their near-optimal performance is proved and further supported by simulation results.

We consider the problem of providing protection against failures in wireless networks by using disjoint paths. Disjoint path routing is commonly used in wired networks for protection, but due to the interference between transmitting nodes in a wireless setting, this approach has not been previously examined for wireless networks. In this paper, we develop a non-disruptive and resource-efficient disjoint path scheme that guarantees protection in wireless networks by utilizing capacity "recapturing" after a failure. Using our scheme, protection can oftentimes be provided for all demands using no additional resources beyond what was required without any protection. We show that the problem of disjoint path protection in wireless networks is not only NP-hard, but in fact remains NP-hard to approximate. We provide an ILP formulation to find an optimal solution, and develop corresponding time-efficient algorithms. Our approach utilizes 87% less protection resources on average than the traditional disjoint path routing scheme. For the case of 2-hop interference, which corresponds to the IEEE 802.11 standard, our protection scheme requires only 8% more resources on average than providing no protection whatsoever.

We consider the problem of transmitting multicast flows with hard deadlines over unreliable wireless channels. Every user in the network subscribes to several multicast flows, and requires a minimum throughput for each subscribed flow to meet the QoS constraints. The network controller schedules the transmissions of multicast traffic based on the instant feedback from the users. We characterize the multicast throughput region by analyzing its boundary points, each of which is the solution to a finite-horizon dynamic programming problem over an exponentially large state space. Using backward induction and interchange arguments, we show that the dynamic programming problems are solved by greedy policies that maximize the immediate weighted sum throughput in every slot. Furthermore, we develop a dynamic throughput-optimal policy that achieves any feasible throughput vector by tracking the running performance received by the users.

Multirate multicast improves user quality but complicates network optimization. This paper introduces a novel control scheme to dynamically optimize multirate multicast. We present MMT, an adaptive policy which combines differential backlog scheduling and intelligent packet dropping, both based on local information. MMT is shown to maximize network throughput by adapting to changing conditions such as channel quality, network congestion, and device capabilities. Then, we study the problem of per-receiver network utility maximization. To maximize sum utility we propose the MMU policy, an extension of MMT with receiver-end flow control. Under the operation of both policies backlog sizes are deterministically bounded, which provides delay guarantees on delivered packets. An important feature of the proposed scheme is that it does not require source cooperation or centralized calculations. To illustrate its practicality, we present a prototype implementation in the NITOS wireless testbed. Experimental results verify the optimality of the scheme and its low complexity.

We consider an opportunistic communication system in which a transmitter selects one of multiple channels over which to schedule a transmission, based on partial knowledge of the network state. We characterize a fundamental limit on the rate that channel state information must be conveyed to the transmitter in order to meet a constraint on expected throughput. This problem is modeled as a causal rate distortion optimization of a Markov source. We introduce a novel distortion metric capturing the impact of imperfect channel state information on throughput. We compute a closed-form expression for the causal information rate distortion function for the case of two channels, as well as an algorithmic upper bound on the causal rate distortion function. Finally, we characterize the gap between the causal information rate distortion and the causal entropic rate-distortion functions.

Legacy networks are often designed to operate with simple single-path routing, like shortest-path, which is known to be throughput suboptimal. On the other hand, previously proposed throughput optimal policies (i.e., backpressure) require every device in the network to make dynamic routing decisions. In this work, we study an overlay architecture for dynamic routing such that only a subset of devices (overlay nodes) need to make dynamic routing decisions. We determine the essential collection of nodes that must bifurcate traffic for achieving the maximum multicommodity network throughput. We apply our optimal node placement algorithm to several graphs and the results show that a small fraction of overlay nodes is sufficient for achieving maximum throughput. Finally, we propose a heuristic policy (OBP), which dynamically controls traffic bifurcations at overlay nodes. In all studied simulation scenarios, OBP not only achieves full throughput, but also reduces delay in comparison to the throughput optimal backpressure routing.

We consider the problem of optimal load balancing in a server farm under overload conditions. A convex penalty minimization problem is studied to optimize queue overflow rates at the servers. We introduce a new class of α-fair penalty functions, and show that the cases of α = 0, 1, ∞ correspond to minimum sum penalty, penalty proportional fairness, and min-max fairness, respectively. These functions are useful to maximize the time to first buffer overflow and minimize the recovery time from temporary overload. In addition, we show that any policy that solves an overload minimization problem with strictly increasing penalty functions must be throughput optimal. A dynamic control policy is developed to solve the overload minimization problem in a stochastic setting. This policy generalizes the well-known join-the-shortest-queue (JSQ) policy and uses intelligent job tagging to optimize queue overflow rates without the knowledge of traffic arrival rates.

We study the problem of scheduling over time varying links in a network that serves both heavy-tailed and light tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic (the heavy queue), and the other receives light-tailed traffic (the light queue). The queues are connected to the server through time-varying ON/OFF links, which model fading wireless channels. We first show that the policy that gives complete priority to the light-tailed traffic guarantees the best possible tail behavior of both queue backlog distributions, whenever the queues are stable. However, the priority policy is not throughput maximizing, and can cause undesirable instability effects in the heavy queue. Next, we study the class of throughput optimal max-weight-α scheduling policies. We discover a threshold phenomenon, and show that the steady state light queue backlog distribution is heavy-tailed for arrival rates above a threshold value, and light-tailed otherwise. We also obtain the exact tail coefficient of the light queue backlog distribution under max-weight-α scheduling. Finally, we study a log-max-weight scheduling policy, which is throughput optimal, and ensures that the light queue backlog distribution is light-tailed.

We study the reliability maximization problem in wavelength division multiplexing (WDM) networks with random link failures. Reliability in these networks is defined as the probability that the logical network is connected, and it is determined by the underlying lightpath routing, network topologies, and the link failure probability. By introducing the notion of lexicographical ordering for lightpath routings, we characterize precise optimization criteria for maximum reliability in the low failure probability regime. Based on the optimization criteria, we develop lightpath routing algorithms that maximize the reliability, and logical topology augmentation algorithms for further improving reliability. We also study the reliability maximization problem in the high failure probability regime.

We consider the problem of scheduling in a single-hop switched network with a mix of heavy-tailed and light-tailed traffic and analyze the impact of heavy-tailed traffic on the performance of Max-Weight scheduling. As a performance metric, we use the delay stability of traffic flows: A traffic flow is delay-stable if its expected steady-state delay is finite, and delay-unstable otherwise. First, we show that a heavy-tailed traffic flow is delay-unstable under any scheduling policy. Then, we focus on the celebrated Max-Weight scheduling policy and show that a light-tailed flow that conflicts with a heavy-tailed flow is also delay-unstable. This is true irrespective of the rate or the tail distribution of the light-tailed flow or other scheduling constraints in the network. Surprisingly, we show that a light-tailed flow can become delay-unstable, even when it does not conflict with heavy-tailed traffic. Delay stability in this case may depend on the rate of the light-tailed flow. Finally, we turn our attention to the class of Max-Weight-α scheduling policies. We show that if the α-parameters are chosen suitably, then the sum of the α-moments of the steady-state queue lengths is finite. We provide an explicit upper bound for the latter quantity, from which we derive results related to the delay stability of traffic flows, and the scaling of moments of steady-state queue lengths with traffic intensity.

We consider a multi-channel communication system in which a transmitter has access to two channels, but does not know the state of either channel. We model the channel state using an ON/OFF Markovian model, and allow the transmitter to probe one of the channels at predetermined probing intervals to decide over which channel to transmit. For models in which the transmitter must transmit over the probed channel, it has been shown that a myopic policy that probes the channel most likely to be ON is optimal. In this work, we allow the transmitter to select a channel over which to transmit that is not necessarily the one it probed. We show that in the case where the two channels are i.i.d, all probing policies yield equal reward. We extend this problem to dynamically choose when to probe based on the results of previous probes, and characterize the optimal policy, as well as provide a LP in terms of state action frequencies to find the optimal policy.

We study the robustness of interdependent networks, in which the state of one network depends on the state of the other network and vice versa. In particular, we focus on the interdependency between the power grid and communication networks, where the grid depends on communications for its control, and the communication network depends on the grid for power. A real-world example is the Italian blackout of 2003, when a small failure in the power grid cascaded between the two networks and led to a massive blackout. In this paper, we study the minimum number of node failures needed to cause total blackout (i.e., all nodes in both networks to fail). In the case of unidirectional interdependency between the networks we show that the problem is NP-hard, and develop heuristics to find a near-optimal solution. On the other hand, we show that in the case of bidirectional interdependency this problem can be solved in polynomial time. We believe that this new interdependency model gives rise to important, yet unexplored, robust network design problems for interdependent networked infrastructures.

We consider distributed strategies for joint routing, scheduling, and network coding to maximize throughput in wireless networks. Network coding allows for an increase in network throughput under certain routing conditions. We previously developed a centralized control policy to jointly optimize for routing and scheduling combined with a simple network coding strategy using max-weight scheduling (MWS) [9]. In this work we focus on pairwise network coding and develop a distributed carrier sense multiple access (CSMA) policy that supports all arrival rates allowed by the network subject to the pairwise coding constraint. We extend our scheme to optimize for packet overhearing to increase the number of beneficial coding opportunities. Simulation results show that the CSMA strategy yields the same throughput as the optimal centralized policy of [9], but at the cost of increased delay. Moreover, overhearing provides up to an additional 25% increase in throughput on random topologies.

We consider the problem of providing network protection that guarantees the maximum amount of time that flow can be interrupted after a failure. This is in contrast to schemes that offer no recovery time guarantees, such as IP rerouting, or the prevalent local recovery scheme of Fast ReRoute, which often over-provisions resources to meet recovery time constraints. To meet these recovery time guarantees, we provide a novel and flexible solution by partitioning the network into failure-independent “recovery domains”, where within each domain, the maximum amount of time to recover from a failure is guaranteed. We show the recovery domain problem to be NP-Hard, and develop an optimal solution in the form of an MILP for both the case when backup capacity can and cannot be shared. This provides protection with guaranteed recovery times using up to 45% less protection resources than local recovery. We demonstrate that the network-wide optimal recovery domain solution can be decomposed into a set of easier to solve subproblems. This allows for the development of flexible and efficient solutions, including an optimal algorithm using Lagrangian relaxation, which simulations show to converge rapidly to an optimal solution. Additionally, an algorithm is developed for when backup sharing is allowed. For dynamic arrivals, this algorithm performs better than the solution that tries to greedily optimize for each incoming demand.

We consider the problem of providing protection against failures in wireless networks subject to interference constraints. Typically, protection in wired networks is provided through the provisioning of backup paths. This approach has not been previously considered in the wireless setting due to the prohibitive cost of backup capacity. However, we show that in the presence of interference, protection can often be provided with no loss in throughput. This is due to the fact that after a failure, links that previously interfered with the failed link can be activated, thus leading to a “recapturing” of some of the lost capacity. We provide both an ILP formulation for the optimal solution, as well as algorithms that perform close to optimal. More importantly, we show that providing protection in a wireless network uses as much as 72% less protection resources as compared to similar protection schemes designed for wired networks, and that in many cases, no additional resources for protection are needed.

We consider utility maximization in networks where the sources do not employ flow control and may consequently overload the network. In the absence of flow control at the sources, some packets will inevitably have to be dropped when the network is in overload. To that end, we first develop a distributed, threshold-based packet dropping policy that maximizes the weighted sum throughput. Next, we consider utility maximization and develop a receiver-based flow control scheme that, when combined with threshold-based packet dropping, achieves the optimal utility. The flow control scheme creates virtual queues at the receivers as a push-back mechanism to optimize the amount of data delivered to the destinations via back-pressure routing. A novel feature of our scheme is that a utility function can be assigned to a collection of flows, generalizing the traditional approach of optimizing per-flow utilities. Our control policies use finite-buffer queues and are independent of arrival statistics. Their near-optimal performance is proved and further supported by simulation results.

Backpressure routing and scheduling, with throughput-optimal operation guarantee, is a promising technique to improve throughput in wireless multi-hop networks. Although backpressure is conceptually viewed as layered, the decisions of routing and scheduling are made jointly, which imposes several challenges in practice. In this work, we present Diff-Max, an approach that separates routing and scheduling and has three strengths: (i) Diff-Max improves throughput significantly, (ii) the separation of routing and scheduling makes practical implementation easier by minimizing cross-layer operations; i.e., routing is implemented in the network layer and scheduling is implemented in the link layer, and (iii) the separation of routing and scheduling leads to modularity; i.e., routing and scheduling are independent modules in Diff-Max, and one can continue to operate even if the other does not. Our approach is grounded in a network utility maximization (NUM) formulation and its solution. Based on the structure of Diff-Max, we propose two practical schemes: Diff-subMax and wDiff-subMax. We demonstrate the benefits of our schemes through simulation in ns-2.

We consider a multi-channel communication system in which a transmitter has access to a large number of channels, but does not know the state of these channels. We model channel state using an ON/OFF Markovian model, and allow the transmitter to probe one of the channels at predetermined probing intervals to decide over which channel to transmit. For models in which the transmitter must send over the probed channel, it has been shown that a myopic policy that probes the channel most likely to be ON is optimal. In this work, we allow the transmitter to select a channel over which to transmit that is not necessarily the one it probed. We show that the myopic policy is not optimal, and propose a simple alternative probing policy, which achieves a higher per-slot expected throughput. Finally, we consider the case where there is a fixed cost associated with probing and derive optimal probing intervals.

We consider a system consisting of N parallel queues, served by one server. Time is slotted, and the server serves one of the queues in each time slot, according to some scheduling policy. We first characterize the exponent of the buffer overflow probability and the most likely overflow trajectories under the Longest Queue First (LQF) scheduling policy. Under statistically identical arrivals to each queue, we show that the buffer overflow exponents can be simply expressed in terms of the total system occupancy exponent of m parallel queues, for some m ≤ N. We next turn our attention to the rate of queue length information needed to operate a scheduling policy, and its relationship to the buffer overflow exponents. It is known that queue length blind policies such as processor sharing and random scheduling perform worse than the queue aware LQF policy, when it comes to buffer overflow probability. However, we show that the overflow exponent of the LQF policy can be preserved with arbitrarily infrequent queue length updates.

We develop a novel network protection scheme that provides guarantees on both the fraction of time a flow has full connectivity, as well as a quantifiable minimum grade of service during downtimes. In particular, a flow can be below the full demand for at most a maximum fraction of time; then, it must still support at least a fraction q of the full demand. This is in contrast to current protection schemes that offer either availability-guarantees with no bandwidth guarantees during the downtime, or full protection schemes that offer 100% availability after a single link failure. We develop algorithms that provide multiple availability guarantees and show that significant capacity savings can be achieved as compared to full protection. If a connection is allowed to drop to 50% of its bandwidth for 1 out of every 20 failures, then a 24% reduction in spare capacity can be achieved over traditional full protection schemes. In addition, for the case of q = 0, corresponding to the standard availability constraint, an optimal pseudo-polynomial time algorithm is presented.

We consider the optimal control problem for networks subjected to time-varying channels, reconfiguration delays, and interference constraints. We model the network by a graph consisting of nodes, links, and a set of link interference constraints, where based on the current network state, the controller decides either to stay with the current link-service configuration or switch to another service configuration at the cost of idling during schedule reconfiguration. Reconfiguration delay occurs in many telecommunications applications and is a new modeling component of this problem that has not been previously addressed. We show that the simultaneous presence of time-varying channels and reconfiguration delays significantly reduces the system stability region and changes the structure of optimal policies. We first consider memoryless channel processes and characterize the stability region in closed form. We prove that a frame-based Max-Weight scheduling algorithm that sets frame durations dynamically, as a function of the current queue sizes and average channel gains is throughput-optimal. Next, we consider arbitrary Markov modulated channel processes and show that memory in the channel processes can be exploited to improve the stability region. We develop a novel approach to characterizing the stability region of such systems using state-action frequencies which are stationary solutions to a Markov Decision Process (MDP) formulation. Finally, we develop a frame-based dynamic control policy, based on the state-action frequencies, and show that it is throughput-optimal asymptotically in the frame length. The FBDC policy is applicable to a broad class of network control systems, with or without reconfiguration delays, and provides a new framework for developing throughput-optimal network control policies using state-action frequencies.

We consider jointly optimal routing, scheduling, and network coding strategies to maximize throughput in wireless networks. While routing and scheduling techniques for wireless networks have been studied for decades, network coding is a relatively new technique that allows for an increase in throughput under certain topological and routing conditions. In this work we introduce k-tuple coding, a generalization of pairwise coding with next-hop decodability, and fully characterize the region of arrival rates for which the network queues can be stabilized under this coding strategy. We propose a dynamic control policy for routing, scheduling, and k-tuple coding, and prove that our policy is throughput optimal subject to the k-tuple coding constraint. We provide analytical bounds on the coding gain of our policy, and present numerical results to support our analytical findings. We show that most of the gains are achieved with pairwise coding, and that the coding gain is greater under 2-hop than 1-hop interference. Simulations show that under 2-hop interference our policy yields median throughput gains of 31% beyond optimal scheduling and routing on random topologies with 16 nodes.

We consider the problem of packet scheduling in a single-hop network with a mix of heavy-tailed and light-tailed traffic, and analyze the impact of heavy-tailed traffic on the performance of Max-Weight scheduling. As a performance metric we use the delay stability of traffic flows: a traffic flow is delay stable if its expected steady-state delay is finite, and delay unstable otherwise. First, we show that a heavy-tailed traffic flow is delay unstable under any scheduling policy. Then, we focus on the celebrated Max-Weight scheduling policy, and show that a light-tailed flow that conflicts with a heavy-tailed flow is also delay unstable. This is true irrespective of the rate or the tail distribution of the light-tailed flow, or other scheduling constraints in the network. Surprisingly, we show that a light-tailed flow can be delay unstable, even when it does not conflict with heavy-tailed traffic. Furthermore, delay stability in this case may depend on the rate of the light-tailed flow. Finally, we turn our attention to the class of Max-Weight-α scheduling policies; we show that if the α-parameters are chosen suitably, then the sum of the α-moments of the steady-state queue lengths is finite. We provide an explicit upper bound for the latter quantity, from which we derive results related to the delay stability of traffic flows, and the scaling of moments of steady-state queue lengths with traffic intensity.

Failures in fiber-optic networks may be caused by natural disasters, such as floods or earthquakes, as well as other events, such as an Electromagnetic Pulse (EMP) attack. These events occur in specific geographical locations, therefore the geography of the network determines the effect of failure events on the network's connectivity and capacity. In this paper we consider a generalization of the min-cut and max-flow problems under a geographic failure model. Specifically, we consider the problem of finding the minimum number of failures, modeled as circular disks, to disconnect a pair of nodes and the maximum number of failure disjoint paths between pairs of nodes. This model applies to the scenario where an adversary is attacking the network multiple times with intention to reduce its connectivity. We present a polynomial time algorithm to solve the geographic min-cut problem and develop an ILP formulation, an exact algorithm, and a heuristic algorithm for the geographic max-flow problem.

We consider a dynamic spectrum access system in which Secondary Users (SUs) choose to either acquire dedicated spectrum or to use spectrum-holes (white spaces) which belong to Primary Users (PUs). The trade-off incorporated in this decision is between immediate yet costly transmission and free but delayed transmission (a consequence of both the possible appearance of PUs and sharing the spectrum holes with multiple SUs). We first consider a system with a single PU band, in which the SU decisions are fixed. Employing queueing-theoretic methods, we obtain explicit expressions for the expected delays associated with using the PU band. Based on that, we then consider self-interested SUs and study the interaction between them as a non-cooperative game. We prove the existence and uniqueness of a symmetric Nash equilibrium, and characterize the equilibrium behavior explicitly. Using our equilibrium results, we show how to maximize revenue from renting dedicated bands to SUs and briefly discuss the extension of our model to multiple PUs. Finally, since spectrum sensing can be resource-consuming, we characterize the gains provided by this capability.

We study the novel hierarchical architecture of Mobile Backbone Networks. In such networks, a set of Mobile Backbone Nodes (MBNs), which are envisioned to be airborne, are deployed to provide an end-to-end communications capability for the terrestrial Regular Nodes (RNs). We address the joint problem of placing a fixed number K MBNs, and assigning each RN to exactly one MBN, using two optimization objectives. The first is the Maximum Fair Placement and Assignment (MFPA) problem in which the objective is to maximize the minimum throughput obtained by any RN. The second is the Maximum Throughput Placement and Assignment (MTPA) problem, in which the objective is to maximize the aggregate throughput of the RNs. We develop an optimal polynomial time algorithm for the MFPA problem for any K, and an optimal polynomial time algorithm for the MTPA problem for K≤ 2. We also develop lower complexity approximation algorithms and present simulation results comparing the performance of the various algorithms.

We consider a dynamic server allocation problem over parallel queues with randomly varying connectivity and server switchover delay between the queues. At each time slot, the server decides either to stay with the current queue or switch to another queue based on the current connectivity and the queue length information. Switchover delay occurs in many telecommunications applications and is a new modeling component of this problem that has not been previously addressed. We show that the simultaneous presence of randomly varying connectivity and switchover delay changes the system stability region and the structure of optimal policies. In the first part of this paper, we consider a system of two parallel queues, and develop a novel approach to explicitly characterize the stability region of the system using state-action frequencies which are stationary solutions to a Markov decision process formulation. We then develop a frame-based dynamic control (FBDC) policy, based on the state-action frequencies, and show that it is throughput optimal asymptotically in the frame length. The FBDC policy is applicable to a broad class of network control systems and provides a new framework for developing throughput-optimal network control policies using state-action frequencies. Furthermore, we develop simple myopic policies that provably achieve more than 90% of the stability region. In the second part of this paper, we extend our results to systems with an arbitrary finite number of queues. In particular, we show that the stability region characterization in terms of state-action frequencies and the throughput optimality of the FBDC policy follows for the general case. Furthermore, we characterize an outer bound on the stability region and an upper bound on sum throughput and show that a simple myopic policy can achieve this sum-throughput upper bound in the corresponding saturated system. Finally, simulation results show that the myopic policies may achieve the full stability region and are more delay efficient than the FBDC policy in most cases.

We develop a distributed throughput-optimal power allocation algorithm in wireless networks. The study of this problem has been limited due to the nonconvexity of the underlying optimization problems that prohibits an efficient solution even in a centralized setting. By generalizing the randomization framework originally proposed for input queued switches to SINR rate-based interference model, we characterize the throughput-optimality conditions that enable efficient and distributed implementation. Using gossiping algorithm, we develop a distributed power allocation algorithm that satisfies the optimality conditions, thereby achieving (nearly) 100 percent throughput. We illustrate the performance of our power allocation solution through numerical simulation.

We investigate the asymptotic behavior of the steady-state queue-length distribution under generalized max-weight scheduling in the presence of heavy-tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic, and the other receives light-tailed traffic. We study the class of throughput-optimal max-weight-$\alpha $scheduling policies and derive an exact asymptotic characterization of the steady-state queue-length distributions. In particular, we show that the tail of the light queue distribution is at least as heavy as a power-law curve, whose tail coefficient we obtain explicitly. Our asymptotic characterization also shows that the celebrated max-weight scheduling policy leads to the worst possible tail coefficient of the light queue distribution, among all nonidling policies. Motivated by the above negative result regarding the max-weight-$\alpha $policy, we analyze a log-max-weight (LMW) scheduling policy. We show that the LMW policy guarantees an exponentially decaying light queue tail while still being throughput-optimal.

This paper considers network control for wireless networks with finite buffers. We investigate the performance of joint flow control, routing, and scheduling algorithms that achieve high network utility and deterministically bounded backlogs inside the network. Our algorithms guarantee that buffers inside the network never overflow. We study the tradeoff between buffer size and network utility and show that under the one-hop interference model, if internal buffers have size$(N-1)/(2 \epsilon)$, then$\epsilon $-optimal network utility can be achieved, where$\epsilon $is a control parameter and$N$is the number of network nodes. The underlying scheduling/routing component of the considered control algorithms requires ingress queue length information (IQI) at all network nodes. However, we show that these algorithms can achieve the same utility performance with delayed ingress queue length information at the cost of a larger average backlog bound. We also show how to extend the results to other interference models and to wireless networks with time-varying link quality. Numerical results reveal that the considered algorithms achieve nearly optimal network utility with a significant reduction in queue backlog compared to existing algorithms in the literature.

This paper addresses the problem of logical topology design for optical backbone networks subject to stochastic traffic demands. The network design problem is broken into three tasks: traffic routing, capacity allocation, and link placement. While the routing and capacity allocation subproblem can be formulated using convex optimization, the link placement component is prohibitive due to its nonlinearity. To address this issue, we develop a linear formulation for the routing and capacity allocation subproblem by extending tools from robust optimization to Gaussian random variables. We show that this linear formulation performs comparably to the optimal nonlinear formulation. Our formulation can then be used to solve the link-placement subproblem for stochastic traffic.

We study the reliability maximization problem in WDM networks with random link failures. Reliability in these networks is defined as the probability that the logical network is connected, and it is determined by the underlying lightpath routing and the link failure probability. We show that in general the optimal lightpath routing depends on the link failure probability, and characterize the properties of lightpath routings that maximize the reliability in different failure probability regimes. In particular, we show that in the low failure probability regime, maximizing the ``cross-layer" min cut of the (layered) network maximizes reliability, whereas in the high failure probability regime, minimizing the spanning tree of the network maximizes reliability. Motivated by these results, we develop lightpath routing algorithms for reliability maximization.

Optical fiber networks consist of fibers that are laid out along physical terrestrial paths. As such, they are vulnerable to geographical physical failures, such as earthquakes and Electromagnetic Pulse (EMP) attacks. Moreover, such disasters can lead to multiple, geographically correlated, failures on the fiber network. Thus, the geographical layout of the fiber infrastructure has a critical impact on the robustness of the network in the face of such geographical physical failures. In this paper, we develop tools to analyze network connectivity after a `random' geographic disaster. The random location of the disaster allows us to model situations where the physical failures are not targeted attacks. In particular, we consider disasters that take the form of a `randomly' located disk in a plane. Using results from geometric probability, we are able to approximate some network performance metrics to such a disaster in polynomial time. We present some numerical results that make clear geographically correlated failures are fundamentally different from independent failures and then discuss network design in the context of random disk-cuts.

We consider a dynamic server control problem for two parallel queues with randomly varying connectivity and server switchover delay between the queues. At each time slot the server decides either to stay with the current queue or switch to the other queue based on the current connectivity and the queue length information. The introduction of switchover time is a new modeling component of this problem, which makes the problem much more challenging. We develop a novel approach to characterize the stability region of the system by using state-action frequencies, which are stationary solutions to a Markov Decision Process (MDP) formulation of the corresponding saturated system. We characterize the stability region explicitly in terms of the connectivity parameters and develop a frame-based dynamic control (FBDC) policy that is shown to be throughput-optimal. In fact, the FBDC policy provides a new framework for developing throughput-optimal network control policies using state-action frequencies. Furthermore, we develop simple Myopic policies that achieve more than 96% of the stability region. Finally, simulation results show that the Myopic policies may achieve the full stability region and are more delay efficient than the FBDC policy in most cases.

We consider scheduling over a wireless system, where the channel state information is not available a priori to the scheduler, but can be inferred from the past. Specifically, the wireless system is modeled as a network of parallel queues. We assume that the channel state of each queue evolves stochastically as an ON/OFF Markov chain. The scheduler, which is aware of the queue lengths but is oblivious of the channel states, has to choose one queue at a time for transmission. The scheduler has no information regarding the current channel states, but can estimate them by using the acknowledgment history. We first characterize the capacity region of the system using tools from Markov Decision Processes (MDP) theory. Specifically, we prove that the capacity region boundary is the uniform limit of a sequence of Linear Programming (LP) solutions. Next, we combine the LP solution with a queue length based scheduling mechanism that operates over long `frames,' to obtain a throughput optimal policy for the system. By incorporating results from MDP theory within the Lyapunov-stability framework, we show that our frame-based policy stabilizes the system for all arrival rates that lie in the interior of the capacity region.

We investigate the asymptotic behavior of the steady-state queue length distribution under generalized max-weight scheduling in the presence of heavy-tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic, and the other receives light-tailed traffic. We study the class of throughput optimal max-weight-α scheduling policies, and derive an exact asymptotic characterization of the steady-state queue length distributions. In particular, we show that the tail of the light queue distribution is heavier than a power-law curve, whose tail coefficient we obtain explicitly. Our asymptotic characterization also shows that the celebrated max-weight scheduling policy leads to the worst possible tail of the light queue distribution, among all non-idling policies. Motivated by the above `negative' result regarding the max-weight-α policy, we analyze a log-max-weight (LMW) scheduling policy. We show that the LMW policy guarantees an exponentially decaying light queue tail, while still being throughput optimal.

This paper presents a scheme in which a dedicated backup network is designed to provide protection from random link failures. Upon a link failure in the primary network, traffic is rerouted through a preplanned path in the backup network. We introduce a novel approach for dealing with random link failures, in which probabilistic survivability guarantees are provided to limit capacity over-provisioning. We show that the optimal backup routing strategy in this respect depends on the reliability of the primary network. Specifically, as primary links become less likely to fail, the optimal backup networks employ more resource sharing amongst backup paths. We apply results from the field of robust optimization to formulate an ILP for the design and capacity provisioning of these backup networks. We then propose a simulated annealing heuristic to solve this problem for largescale networks, and present simulation results that verify our analysis and approach.

This paper develops a mesh network protection scheme that guarantees a quantifiable minimum grade of service upon a failure within a network. The scheme guarantees that a fraction q of each demand remains after any single link failure. A linear program is developed to find the minimum-cost capacity allocation to meet both demand and protection requirements. For q ≤ 1/2, an exact algorithmic solution for the optimal routing and allocation is developed using multiple shortest paths. For q >; 1/2, a heuristic algorithm based on disjoint path routing is developed that performs, on average, within 1.4% of optimal, and runs four orders of magnitude faster than the minimum-cost solution achieved via the linear program. Moreover, the partial protection strategies developed achieve reductions of up to 82% over traditional full protection schemes.

This paper considers the scheduling problem for networks with interference constraints and switchover delays, where it takes a nonzero time to reconfigure each service schedule. Switchover delay occurs in many telecommunication applications such as satellite, optical or delay tolerant networks (DTNs). Under zero switchover delay it is well known that the Max-Weight algorithm is throughput-optimal without requiring knowledge of the arrival rates. However, we show that this property of Max-Weight no longer holds when there is a nonzero switchover delay. We propose a class of variable frame based Max-Weight (VFMW) algorithms which employ the Max-Weight schedule corresponding to the beginning of the frame during an interval of duration dependent on the queue sizes. The VFMW algorithms dynamically adapt the frame sizes to the stochastic arrivals and provide throughput-optimality without requiring knowledge of the arrival rates. Numerical results regarding the application of the VFMW algorithms to DTN and optical networks demonstrate a good delay performance.

We consider a dynamic spectrum access system in which Secondary Users (SUs) choose to either acquire dedicated spectrum or to use spectrum-holes (white spaces) which belong to Primary Users (PUs). The tradeoff incorporated in this decision is between immediate yet costly transmission and free but delayed transmission (a consequence of both the possible appearance of PUs and sharing the spectrum holes with multiple SUs). We first consider a system with a single PU band, in which the SU decisions are fixed. Employing queueing-theoretic methods, we obtain explicit expressions for the expected delays associated with using the PU band. Based on that, we then consider self-interested SUs and study the interaction between them as a noncooperative game. We prove the existence and uniqueness of a symmetric Nash equilibrium, and characterize the equilibrium behavior explicitly. Using our equilibrium results, we show how to maximize revenue from renting dedicated bands to SUs. Finally, we extend the scope to a scenario with multiple PUs, show that the band-pricing analysis can be applied to some special cases, and provide numerical examples.

We study the role played by queue length information in the operation of flow control and server allocation policies. We first consider a simple model of a single server queue with congestion-based flow control. The input rate at any instant is decided by a flow control policy, based on the queue occupancy. We identify a simple “two-threshold” control policy, which achieves the best possible exponential scaling for the queue congestion probability, for any rate of control. We show that when the control channel is reliable, the control rate needed to ensure the optimal decay exponent for the congestion probability can be made arbitrarily small. However, if control channel erasures occur probabilistically, we show the existence of a critical erasure probability threshold beyond which the congestion probability undergoes a drastic increase due to the frequent loss of control packets. We also determine the optimal amount of error protection to apply to the control signals by using a simple bandwidth sharing model. Finally, we show that the queue length based server allocation problem can also be treated using this framework and that the results obtained for the flow control setting can also be applied to the server allocation case.

This paper describes new algorithms for throughput optimization in a mobile backbone network. This hierarchical communication framework combines mobile backbone nodes, which have superior mobility and communication capability, with regular nodes, which are constrained in mobility and communication capability. An important quantity of interest in mobile backbone networks is the number of regular nodes that can be successfully assigned to mobile backbone nodes at a given throughput level. This paper develops a novel technique for maximizing this quantity in networks of fixed regular nodes using mixed-integer linear programming (MILP). The MILP-based algorithm provides a significant reduction in computation time compared to existing methods and is computationally tractable for problems of moderate size. An approximation algorithm is also developed that is appropriate for large-scale problems. This paper presents a theoretical performance guarantee for the approximation algorithm and also demonstrates its empirical performance. Finally, the mobile backbone network problem is extended to include mobile regular nodes, and exact and approximate solution algorithms are presented for this extension.

We consider network reliability in layered networks where the lower layer experiences random link failures. In layered networks, each failure at the lower layer may lead to multiple failures at the upper layer. We generalize the classical polynomial expression for network reliability to the multilayer setting. Using random sampling techniques, we develop polynomial-time approximation algorithms for the failure polynomial. Our approach gives an approximate expression for reliability as a function of the link failure probability, eliminating the need to resample for different values of the failure probability. Furthermore, it gives insight on how the routings of the logical topology on the physical topology impact network reliability. We show that maximizing the min cut of the (layered) network maximizes reliability in the low-failure-probability regime. Based on this observation, we develop algorithms for routing the logical topology to maximize reliability.

In layered networks, a single failure at a lower layer may cause multiple failures in the upper layers. As a result, traditional schemes that protect against single failures may not be effective in multilayer networks. In this paper, we introduce the problem of maximizing the connectivity of layered networks. We show that connectivity metrics in layered networks have significantly different meaning than their single-layer counterparts. Results that are fundamental to survivable single-layer network design, such as the Max-Flow Min-Cut Theorem, are no longer applicable to the layered setting. We propose new metrics to measure connectivity in layered networks and analyze their properties. We use one of the metrics, Min Cross Layer Cut, as the objective for the survivable lightpath routing problem and develop several algorithms to produce lightpath routings with high survivability. This allows the resulting cross-layer architecture to be resilient to failures between layers.

Communication networks are vulnerable to natural disasters, such as earthquakes or floods, as well as to physical attacks, such as an electromagnetic pulse (EMP) attack. Such real-world events happen in specific geographical locations and disrupt specific parts of the network. Therefore, the geographical layout of the network determines the impact of such events on the network's connectivity. In this paper, we focus on assessing the vulnerability of (geographical) networks to such disasters. In particular, we aim to identify the most vulnerable parts of the network. That is, the locations of disasters that would have the maximum disruptive effect on the network in terms of capacity and connectivity. We consider graph models in which nodes and links are geographically located on a plane. First, we consider a simplistic bipartite graph model and present a polynomial-time algorithm for finding a worst-case vertical line segment cut. We then generalize the network model to graphs with nodes at arbitrary locations. We model the disaster event as a line segment or a disk and develop polynomial-time algorithms that find a worst-case line segment cut and a worst-case circular cut. Finally, we obtain numerical results for a specific backbone network, thereby demonstrating the applicability of our algorithms to real-world networks. Our novel approach provides a promising new direction for network design to avert geographical disasters or attacks.

This paper considers network control for wireless networks with finite buffers. We investigate the performance of joint flow control, routing, and scheduling algorithms which achieve high network utility and deterministically bounded backlogs inside the network. Our algorithms guarantee that buffers inside the network never overflow. We study the tradeoff between buffer size and network utility and show that if internal buffers have size (N - 1)/¿ then a high fraction of the maximum utility can be achieved, where ¿ captures the loss in utility and N is the number of network nodes. The underlying scheduling/routing component of the considered control algorithms requires ingress queue length information (IQI) at all network nodes. However, we show that these algorithms can achieve the same utility performance with delayed ingress queue length information. Numerical results reveal that the considered algorithms achieve nearly optimal network utility with a significant reduction in queue backlog compared to the existing algorithm in the literature. Finally, we discuss extension of the algorithms to wireless networks with time-varying links.

We consider network reliability in layered networks where the lower layer experiences random link failures. In layered networks, each failure at the lower layer may lead to multiple failures at the upper layer. We generalize the classical polynomial expression for network reliability to the multi-layer setting. Using random sampling techniques, we develop polynomial time approximation algorithms for the failure polynomial. Our approach gives an approximate expression for reliability as a function of the link failure probability, eliminating the need to resample for different values of the failure probability. Furthermore, it gives insight on how the routings of the logical topology on the physical topology impact network reliability. We show that maximizing the min cut of the (layered) network maximizes reliability in the low failure probability regime. Based on this observation, we develop algorithms for routing the logical topology to maximize reliability.

Fiber-optic networks are vulnerable to natural disasters, such as tornadoes or earthquakes, as well as to physical failures, such as an anchor cutting underwater fiber cables. Such real-world events occur in specific geographical locations and disrupt specific parts of the network. Therefore, the geography of the network determines the effect of physical events on the network's connectivity and capacity. In this paper, we develop tools to analyze network failures after a `random' geographic disaster. The random location of the disaster allows us to model situations where the physical failures are not targeted attacks. In particular, we consider disasters that take the form of a `random' line in a plane. Using results from geometric probability, we are able to calculate some network performance metrics to such a disaster in polynomial time. In particular, we can evaluate average two-terminal reliability in polynomial time under `random' line-cuts. This is in contrast to the case of independent link failures for which there exists no known polynomial time algorithm to calculate this reliability metric. We also present some numerical results to show the significance of geometry on the survivability of the network and discuss network design in the context of random line-cuts. Our novel approach provides a promising new direction for modeling and designing networks to lessen the effects of geographical disasters or attacks.

We investigate the performance of longest-queue-first (LQF) scheduling (i.e., greedy maximal scheduling) for wireless networks under the SINR interference model. This interference model takes network geometry and the cumulative interference effect into account, which, therefore, capture the wireless interference more precisely than binary interference models. By employing the ρ-local pooling technique, we show that LQF scheduling achieves zero throughput in the worst case. We then propose a novel technique to localize interference which enables us to decentralize the LQF scheduling while preventing it from having vanishing throughput in all network topologies. We characterize the maximum throughput region under interference localization and present a distributed LQF scheduling algorithm. Finally, we present numerical results to illustrate the usefulness and to validate the theory developed in the paper.

The physical layer of future wireless networks will be based on novel radio technologies such as UWB and MIMO. One of the important capabilities of such technologies is the ability to capture a few packets simultaneously. This capability has the potential to improve the performance of the MAC layer. However, we show that in networks with spatially distributed nodes, reusing backoff mechanisms originally designed for narrow-band systems (e.g., CSMA/CA) is inefficient. It is well known that when networks with spatially distributed nodes operate with such MAC protocols, the channel may be captured by nodes that are near the destination, leading to unfairness. We show that when the physical layer enables multipacket reception, the negative implications of reusing the legacy protocols include not only such unfairness, but also a significant throughput reduction. We present alternative backoff mechanisms and evaluate their performance via Markovian analysis, approximations, and simulation. We show that our alternative backoff mechanisms can improve both overall throughput and fairness.

We develop diverse routing schemes for dealing with multiple, possibly correlated, failures. While disjoint path protection can effectively deal with isolated single link failures, recovering from multiple failures is not guaranteed. In particular, events such as natural disasters or intentional attacks can lead to multiple correlated failures, for which recovery mechanisms are not well understood. We take a probabilistic view of network failures where multiple failure events can occur simultaneously, and develop algorithms for finding diverse routes with minimum joint failure probability. Moreover, we develop a novel Probabilistic Shared Risk Link Group (PSRLG) framework for modeling correlated failures. In this context, we formulate the problem of finding two paths with minimum joint failure probability as an integer nonlinear program (INLP) and develop approximations and linear relaxations that can find nearly optimal solutions in most cases.

The goal of this paper is to characterize the tradeoff between the rate of control and network congestion for flow control policies. We consider a simple model of a single server queue with congestion-based flow control. The input rate at any instant is decided by a flow control policy, based on the queue occupancy. We identify a simple 'two threshold' control policy, which achieves the best possible congestion probability, for any rate of control. We show that in the absence of control channel errors, the control rate needed to ensure the optimal decay exponent for the congestion probability can be made arbitrarily small. However, if control channel errors occur probabilistically, we show the existence of a critical error probability threshold beyond which the congestion probability undergoes a drastic increase due to the frequent loss of control packets. Finally, we determine the optimal amount of error protection to apply to the control signals by using a simple bandwidth sharing model.

In layered networks, a single failure at a lower layer may cause multiple failures in the upper layers. As a result, traditional schemes that protect against single failures may not be effective in cross-layer networks. In this paper, we introduce the problem of maximizing the connectivity of layered networks. We show that connectivity metrics in layered networks have significantly different meaning than their single-layer counterparts. Results that are fundamental to survivable single-layer network design, such as the Max-Flow Min-Cut theorem, are no longer applicable to the layered setting. We propose new metrics to measure connectivity in layered networks and analyze their properties. We use one of the metrics, Min Cross Layer Cut, as the objective for the survivable lightpath routing problem, and develop several algorithms to produce lightpath routings with high survivability. This allows the resulting cross-layer architecture to be resilient to failures.

We develop diverse routing schemes for dealing with multiple, possibly correlated, failures. While disjoint path protection can effectively deal with isolated single link failures, recovering from multiple failures is not guaranteed. In particular, events such as natural disasters or intentional attacks can lead to multiple correlated failures, for which recovery mechanisms are not well understood. We take a probabilistic view of network failures where multiple failure events can occur simultaneously, and develop algorithms for finding diverse routes with minimum joint failure probability. Moreover, we develop a novel Probabilistic Shared Risk Link Group (PSRLG) framework for modeling correlated failures. In this context, we formulate the problem of finding two paths with minimum joint failure probability as an Integer Non-Linear Program (INLP), and develop approximations and linear relaxations that can find nearly optimal solutions in most cases.

Communication networks are vulnerable to natural disasters, such as earthquakes or floods, as well as to physical attacks, such as an Electromagnetic Pulse (EMP) attack. Such real- world events happen in specific geographical locations and disrupt specific parts of the network. Therefore, the geographical layout of the network determines the impact of such events on the network's connectivity. In this paper, we focus on assessing the vulnerability of (geographical) networks to such disasters. In particular, we aim to identify the most vulnerable parts of the network. That is, the locations of disasters that would have the maximum disruptive effect on the network in terms of capacity and connectivity. We consider graph models in which nodes and links are geographically located on a plane, and model the disaster event as a line segment or a circular cut. We develop algorithms that find a worst- case line segment cut and a worst-case circular cut. Then, we obtain numerical results for a specific backbone network, thereby demonstrating the applicability of our algorithms to real-world networks. Our novel approach provides a promising new direction for network design to avert geographical disasters or attacks.

In this paper, we consider a distributed one-hop wireless network with n pairs of transmitters and receivers. It is assumed that each transmitter/receiver node is only connected to k receiver/transmitter nodes which are defined as neighboring nodes. The channel between the neighboring nodes is assumed to be Rayleigh fading. The objective is to find the maximum achievable sum-rate of the network in the asymptotic case of n, k ¿ ¿. It is shown that the asymptotic throughput of the system scales as n log k/k. An opportunistic on-off scheduling is proposed and shown to be asymptotically throughput optimal.

We consider throughput-optimal power allocation in multi-hop wireless networks. The study of this problem has been limited due to the non-convexity of the underlying optimization problems, that prohibits an efficient solution even in a centralized setting. We take a randomization approach to deal with this difficulty. To this end, we generalize the randomization framework originally proposed for input queued switches to an SINR rate-based interference model. Further, we develop distributed power allocation and comparison algorithms that satisfy these conditions, thereby achieving (nearly) 100% throughput. We illustrate the performance of our proposed power allocation solution through numerical investigation and present several extensions for the considered problem.

We study a novel hierarchical wireless networking approach in which some of the nodes are more capable than others. In such networks, the more capable nodes can serve as mobile backbone nodes and provide a backbone over which end-to-end communication can take place. Our approach consists of controlling the mobility of the backbone nodes in order to maintain connectivity. We formulate the problem of minimizing the number of backbone nodes and refer to it as the Connected Disk Cover (CDC) problem. We show that it can be decomposed into the Geometric Disk Cover (GDC) problem and the Steiner Tree Problem with Minimum Number of Steiner Points (STP-MSP). We prove that if these subproblems are solved separately by gamma- and delta-approximation algorithms, the approximation ratio of the joint solution is gamma+delta. Then, we focus on the two subproblems and present a number of distributed approximation algorithms that maintain a solution to the GDC problem under mobility. A new approach to the solution of the STP-MSP is also described. We show that this approach can be extended in order to obtain a joint approximate solution to the CDC problem. Finally, we evaluate the performance of the algorithms via simulation and show that the proposed GDC algorithms perform very well under mobility and that the new approach for the joint solution can significantly reduce the number of mobile backbone nodes.

The physical layer of future wireless networks will be based on novel radio technologies such as UWB and MIMO. One of the important capabilities of such technologies is the ability to capture a few packets simultaneously. This capability has the potential to improve the performance of the MAC layer. However, we show that in networks with spatially distributed nodes, reusing backoff mechanisms originally designed for narrow-band systems (e.g. CSMA/CA) is inefficient. It is well known that when networks with spatially distributed nodes operate with such MAC protocols, the channel may be captured by nodes that are near the destination, leading to unfairness. We show that when the physical layer enables multipacket reception, the negative implications of reusing the legacy protocols include not only such unfairness but also a significant throughput reduction. We present alternative backoff mechanisms and evaluate their performance via Markovian analysis and simulation. We show that our alternative backoff mechanisms can improve both overall throughput and fairness.

We study the novel hierarchical architecture of Mobile Backbone Networks. In such networks, a set of mobile backbone nodes (MBNs) are deployed to provide an end-to-end communications capability for the regular nodes (RNs). In this work, we address the joint problem of placing a fixed number K MBNs in the plane, and assigning each RN to exactly one MBN. We formulate and solve two problems under a general communications model. The first is the maximum fair placement and assignment (MFPA) problem in which the objective is to maximize the throughput of the minimum throughput RN. The second is the maximum throughput placement and assignment (MTPA) problem, in which the objective is to maximize the aggregate throughput of the RNs. Our main result is a novel optimal polynomial time algorithm for the MFPA problem for fixed K. For a restricted version of the MTPA problem, we develop an optimal polynomial time algorithm for Kles2. We also develop two heuristic algorithms for both problems, including an approximation algorithm for which we bound the worst case performance loss. Finally, we present simulation results comparing the performance of the various algorithms developed in the paper.

Efficient operation of wireless networks requires distributed routing and scheduling algorithms that take into account interference constraints. Recently, a few algorithms for networks with primary- or secondary-interference constraints have been developed. Due to their distributed operation, these algorithms can achieve only a guaranteed fraction of the maximum possible throughput. It was also recently shown that if a set of conditions (known as Local Pooling) is satisfied, simple distributed scheduling algorithms achieve 100% throughput. However, previous work regarding Local Pooling focused mostly on obtaining abstract conditions and on networks with single-hop interference or single-hop traffic. In this paper, we identify several graph classes that satisfy the Local Pooling conditions, thereby enabling the use of such graphs in network design algorithms. Then, we study the multihop implications of Local Pooling. We show that in many cases, as the interference degree increases, the Local Pooling conditions are more likely to hold. Consequently, although increased interference reduces the maximum achievable throughput of the network, it tends to enable distributed algorithms to achieve 100% of this throughput. Regarding multihop traffic, we show that if the network satisfies only the single-hop Local Pooling conditions, distributed joint routing and scheduling algorithms are not guaranteed to achieve maximum throughput. Therefore, we present new conditions for Multihop Local Pooling, under which distributed algorithms achieve 100% throughout. Finally, we identify network topologies in which the conditions hold and discuss the algorithmic implications of the results.

We study energy-efficient transmission of data with deadline constraints over a time-varying channel. Specifically, the system model consists of a wireless transmitter with controllable transmission rate, time-varying and stochastic channel state, and strict delay constraints on the packets in the queue. While the transmitter can control the rate, the transmission power required depends on the chosen rate and the prevailing channel condition. The objective is to obtain a rate control policy that serves the data within the deadline constraints while minimizing the total energy expenditure. Toward this end, we first introduce the canonical problem of transmitting B units of data by deadline T over a Markov fading channel, and obtain the optimal policy for it using continuous-time stochastic control theory. Using a novel cumulative curves methodology and a decomposition approach, we extend the above setup to consider extensions involving variable deadlines on the packets. Finally, utilizing the analysis we present a heuristic policy for the case of arbitrary packet arrivals to the queue with individual deadline constraints, and give illustrative simulation results for its performance.

We study the problem of communication reliability of wireless networks in a fading environment based on the outage probability formulation. The exact expression for the disconnect probability, the probability that a transmission by a node is not received correctly by any other node in the network, is obtained for one and two dimensional random networks. We obtain the end-to-end reliability of multi-hop transmission using the outage probability metric and develop algorithms for finding the most reliable route subject to power constraints as well as the minimum energy route subject to a reliability constraint. Finally, we study the tradeoff between outage probability and transmission power, with and without route diversity.

In this paper, we provide and study a general framework that allows the development of distributed mechanisms to achieve full utilization of multi-hop wireless networks. In particular, we describe a generic randomized routing, scheduling and flow control scheme that is applicable to a large class of interference models, and that allows for the development of distributed algorithms which maximize network throughput and utilization. In particular, we focus on a specific interference model, namely the secondary interference model, and develop distributed algorithms with polynomial communication and computation complexity in the network size. This is an important result given that earlier throughput-optimal algorithms developed for such a model relies on the solution to an NP-hard problem. This results in a polynomial complexity cross-layer algorithm that achieves throughput optimality and fair allocation of network resources amongst the users. We further show that our algorithmic approach enables us to efficiently approximate the capacity region of a multi-hop wireless network.

We study the problem of efficiently scheduling users in a Gaussian broadcast channel withMtransmit antennas andKindependent receivers, each with a single antenna. We first focus on a scenario with two transmit antennas and statistically identical users, and analyze the gap between the full sum capacity and the rate that can be achieved by transmitting to a suitably selected pair of users. In particular, we consider a scheme that picks the user with the largest channel gain, and selects a second user from the nextL- 1 strongest ones to form the best pair, taking channel orientations into account as well. We prove that the expected rate gap converges to 1/(L- 1) nats/symbol when the total number of usersKtends to infinity. AllowingLto increase withK, it may be deduced that transmitting to a properly chosen pair of users is asymptotically optimal, while considerably reducing the feedback overhead and scheduling complexity. Next, we tackle the problem of maximizing aweightedsum rate in a scenario with heterogeneous user characteristics. We establish a novel upper bound for the weighted sum capacity, which we then use to show that the maximum expected weighted sum rate can be asymptotically achieved by transmitting to a suitably selected subset of at mostMCusers, whereCdenotes the number of distinct user classes. Numerical experiments indicate that the asymptotic results are remarkably accurate and that the proposed schemes operate close to absolute performance bounds, even for a moderate number of users.

We study the problem of transmission-side diversity and routing in a static wireless network. It is assumed that each node in the network is equipped with a single omnidirectional antenna and that multiple nodes are allowed to coordinate their transmissions in order to obtain energy savings. We derive analytical results for achievable energy savings for both line and grid network topologies. It is shown that the energy savings of and are achievable in line and grid networks with a large number of nodes, respectively. We then develop a dynamic-programming-based algorithm for finding the optimal route in an arbitrary network, as well as suboptimal algorithms with polynomial complexity. We show through simulations that these algorithms can achieve average energy savings of about in random networks, as compared to the noncooperative schemes.

We consider a slotted system with N queues, and independent and identically distributed (i.i.d.) Bernoulli arrivals at each queue during each slot. Each queue is associated with a channel that changes between "on" and "off" states according to i.i.d. Bernoulli processes. We assume that the system has K identical transmitters ("servers"). Each server, during each slot, can transmit up to C packets from each queue associated with an "on" channel. We show that a policy that assigns the servers to the longest queues whose channel is "on" minimizes the total queue size, as well as a broad class of other performance criteria. We provide several extensions, as well as some qualitative results for the limiting case where N is very large. Finally, we consider a "fluid" model under which fractional packets can be served, and subject to a constraint that at most C packets can be served in total from all of the N queues. We show that when K=N, there is an optimal policy which serves the queues so that the resulting vector of queue lengths is "Most Balanced" (MB)

We address multi-user scheduling over the downlink channel in wireless data systems. Specifically, we consider a time-slotted system with a single transmitter serving multiple users, where the channel condition of each user is time varying. Based on the throughput requirements, the user set is divided into two classes (i) throughput guaranteed (QoS) users, and, (ii) best effort (BE) users. For this system we obtain the optimal policy that serves the QoS users with the minimum time-slot utilization and maximizes the total fraction of time-slots allocated to the BE users. We show that the optimal policy has a simple geometric structure that can be easily visualized graphically. In the special case of Rayleigh fading, we obtain closed-form formulas that relate the achievable throughput-rate guarantee of the QoS users as a function of other system parameters, thus, providing closed-from relationships to understand the various system tradeoffs. Analytical comparison between the optimal and the random-scheduling policy shows that gains on the order of ln(N) can be achieved, where N is the number of QoS users. Finally, we present simulation results comparing the optimal policy under Rayleigh and Nakagami fading with other heuristic policies including a well known opportunistic-scheduling policy.

We study the maximum throughput properties of dynamically reconfigurable optical networks having wavelength and port constraints. Using stability as the throughput performance metric, we outline the single-hop and multi-hop stability regions of the network. We describe throughput-optimal dynamic algorithms employing joint WDM reconfiguration and electronic layer routing decisions. Our approach is a generalization of the BvN decomposition technique that has been so effective at expressing any stabilizable rate matrix for input-queued switches as a convex combination of service configurations. We consider generalized decompositions for physical topologies with wavelength and port constraints. For the case of a single wavelength per optical fiber, we link the decomposition problem to a corresponding Routing and Wavelength Assignment (RWA) problem. We characterize the stability region of the reconfigurable network, employing both single-hop and multi- hop routing, in terms of the RWA problem applied to the same physical topology. We derive expressions for two geometric properties of the stability region: maximum stabilizable uniform arrival rate, and maximum scaled doubly substochastic region. These geometric properties provide a measure of the performance gap between a network having a single wavelength per optical fiber and its wavelength-unconstrained version. They also provide a measure of the performance gap between algorithms employing single-hop versus multi-hop electronic routing.

This paper considers the interaction between channel assignment and distributed scheduling in multi-channel multiradio Wireless Mesh Networks (WMNs). Recently, a number of distributed scheduling algorithms for wireless networks have emerged. Due to their distributed operation, these algorithms can achieve only a fraction of the maximum possible throughput. As an alternative to increasing the throughput fraction by designing new algorithms, in this paper we present a novel approach that takes advantage of the inherent multi-radio capability of WMNs. We show that this capability can enable partitioning of the network into subnetworks in which simple distributed scheduling algorithms can achieve 100% throughput. The partitioning is based on the recently introduced notion of Local Pooling. Using this notion, we characterize topologies in which 100% throughput can be achieved distributedly. These topologies are used in order to develop a number of channel assignment algorithms that are based on a matroid intersection algorithm. These algorithms partition a network in a manner that not only expands the capacity regions of the subnetworks but also allows distributed algorithms to achieve these capacity regions. Finally, we evaluate the performance of the algorithms via simulation and show that they significantly increase the distributedly achievable capacity region.

We study a novel hierarchical wireless networking approach in which some of the nodes are more capable than others.In such networks,the more capable nodes can serve as Mobile Backbone Nodes and provide a backbone over which end-to-end communication can take place. Our approac consists of controlling the mobility of the Backbone Nodes in order to maintain connectivity. We formulate the problem of minimizing the number of backbone nodes and refer to it as the Connected Disk Cover problem.We show that it can be decomposed into the Geometric Disk Cover (GDC)problem and the Steiner Tree Problem wit Minimum Number of Steiner Points (STP-MSP). We prove that if these sub-problems are solved separately by γ- and δ- approximation algorithms, the approximation ratio of t e joint solution is γ + δ. Then, we focus on the two subproblems and present a number of distributed approximation algorithms that maintain a solution to the GDC problem under mobility A new approach to the solution of the STP-MSP is also described. We show that this approach can be extended in order to obtain a joint approximate solution to the Connected Disk Cover problem. Finally, we evaluate the performance of the algorithms via simulation and show that the proposed GDC algorithms perform very well under mobility and that the new approac for the joint solution can significantly reduce the number of required Mobile Backbone Nodes.

The capacity region of the Gaussian multi-antenna broadcast channel was characterized recently in [19]. It was shown that a scheme based on Dirty Paper Coding [2] achieves the full capacity region when the transmitter has perfect channel state information. However, this scheme potentially involves considerable amounts of feedback and complex algorithms for coding and user selection. This has led to a quest for practical transmission schemes and ways to reduce the amount of channel state information required. In particular, it has been shown that when the total number of users is large, the sum capacity can be closely approached by transmitting to a small subset of near-orthogonal users. In order to further quantify the latter observation, we study a Gaussian broadcast channel with two transmit antennas and K statistically identical, independent users each with a single receive antenna. We obtain an exact asymptotic characterization of the gap between the full sum capacity and the rate that can be achieved by transmitting to a suitably selected pair of users. Specifically, we consider various simple schemes for user-pair selection that take into account the channel norms as well as the relative orientation of the channel vectors. We conclude that a scheme that picks the strongest user and selects a second user to form the best pair, is asymptotically optimal, while also being attractive in terms of feedback and operational complexity.

We develop a novel auction-based algorithm to allow users to fairly compete for a wireless fading channel. We use the second-price auction mechanism whereby user bids for the channel, during each time slot, based on the fade state of the channel, and the user that makes the highest bid wins use of the channel by paying the second highest bid. Under the assumption that each user has a limited budget for bidding, we show the existence of a Nash equilibrium strategy, and the Nash equilibrium leads to a unique allocation for certain channel state distribution, such as the exponential distribution and the uniform distribution over [0, 1]. For uniformly distributed channel state, we establish that the aggregate throughput received by the users using the Nash equilibrium strategy is at least 3/4 of what can be obtained using an optimal centralized allocation that does not take fairness into account. We also show that the Nash equilibrium strategy leads to an allocation that is Pareto optimal (i.e., it is impossible to make some users better off without making some other users worse off). Based on the Nash equilibrium strategies of the second-price auction with money constraint, we further propose a centralized opportunistic scheduler that does not suffer the shortcomings associated with the proportional fair scheduler.

We seek to maximize the average data throughput of a single transmitter sending data over a fading channel to a single user class. The transmitter has a fixed amount of energy and a limited amount of time to send data. Given that the channel state determines the throughput obtained per unit of energy expended, the goal is to obtain a policy for scheduling transmissions that maximizes the expected data throughput. We develop a dynamic programming formulation that leads to an optimal transmission schedule, first where the present channel state is known just before transmission, and then to the case where the current channel state is unknown before transmission, but observed after transmission and evolves according to a Markov process. We then extend our approach to the problem of minimizing the expected energy required to send a fixed amount of data over a fading channel given deadline constraints.

We consider a multi-hop wireless network with a connection-oriented traffic model and multiple transmission channels that can be spatially re-used. In such a network the blocking probability of a call that makes a channel request depends on (a) the channel assignment scheme and (b) the transmission radius of the nodes which affects the network link structure. In this work, we study these two aspects for simple wireless networks. Specifically, we develop blocking probability analysis for a wireless line and grid network and explore the tradeoff between transmission radius and blocking probability for multi-hop calls. We show that for a line network a larger transmission radius can substantially reduce the blocking probability of calls, while for a grid network with a more dense node topology using a smaller transmission radius is better. We then, investigate various channel assignment schemes and present a novel non-rearranging channel assignment algorithm for multi-hop calls in a general network. Our algorithm efficiently incorporates spatial channel re-use and significantly reduces call blocking probability when compared to other algorithms.

We compare the effectiveness of uniform versus non-uniform waveband switching under the dual cost metrics of switching requirements and fiber capacity. We consider a star topology and begin by characterizing the optimal performance frontier achievable under no restrictions on waveband sizing, and provide algorithms employing non-uniform waveband sizing that approach or achieve this optimum. We then consider the special case of uniform waveband sizing, and show that the performance compares very favorably. We also extend our results to general topologies.

We present a game-theoretical model of a wireless communication system with multiple competing users sharing a multi-access fading channel. With a specified capture rule and a limited amount of energy available, a user opportunistically adjusts its transmission power based on its own channel state to maximize the user's own individual throughput. We derive an explicit form of the Nash equilibrium power allocation strategy. Furthermore, this Nash equilibrium power allocation strategy is unique under certain capture rule. We also quantify the loss of efficiency in throughput due to user's selfish behavior. Moreover, as the number of users in the system increases, the total system throughput obtained by using a Nash equilibrium strategy approaches the maximum attainable throughput.

We develop algorithms for joint IP layer routing and WDM logical topology reconfiguration in IP-over-WDM networks experiencing stochastic traffic. At the WDM layer, we associate a non-negligible tuning latency with WDM reconfiguration, during which time tuned transceivers cannot service backlogged data. The IP layer is modeled as a queueing system. We demonstrate that our algorithms achieve asymptotic throughput optimality by using frame-based maximum weight scheduling decisions. We study both deterministic and random frame durations. In addition to dynamically triggering WDM reconfiguration, our algorithms specify precisely how to route packets over the IP layer during the phases in which the WDM layer remains fixed. Our algorithms remain valid under a variety of optical layer constraints. We provide an analysis of the specific case of WDM networks with multiple ports per node. In order to gauge the delay properties of our algorithms, we conduct a simulation study and demonstrate an important tradeoff between WDM reconfiguration and IP layer routing. We find that multi-hop routing is extremely beneficial at low throughput levels, while single-hop routing achieves improved delay at high throughput levels. For a simple access network, we demonstrate through simulation the benefit of employing multi-hop IP layer routes.

We consider optimal control for general networks with both wireless and wireline components and time varying channels. A dynamic strategy is developed to support all traffic whenever possible, and to make optimally fair decisions about which data to serve when inputs exceed network capacity. The strategy is decoupled into separate algorithms for flow control, routing, and resource allocation, and allows each user to make decisions independent of the actions of others. The combined strategy is shown to yield data rates that are arbitrarily close to the optimal operating point achieved when all network controllers are coordinated and have perfect knowledge of future events. The cost of approaching this fair operating point is an end-to-end delay increase for data that is served by the network. Analysis is performed at the packet level and considers the full effects of queueing.

We consider a queueing system with controllable service rate; for example, a transmitter whose rate can be controlled by varying the transmission power. For such a system we obtain optimal data transmission policies that satisfy given quality of service (QoS) constraints and also minimize the total transmission energy expenditure. First, we consider the deterministic case of known arrivals and present a formulation based on a calculus approach using arrival and minimum departure curves. The problem is posed as a continuous time optimization and an optimal solution is obtained for general arrival curves and QoS constraints. In the latter half of the paper, we consider a stochastic arrival process (Poisson process) and a single deadline constraint. The objective is to obtain a transmission policy that minimizes the expected energy expenditure. The problem is formulated as a stochastic optimal control problem and an explicit solution is obtained with some relaxation. Finally, simulation results comparing various policies are presented.

We consider the problem of transmission scheduling of data over a wireless fading channel with hard deadline constraints. Our system consists of N users, each with a fixed amount of data that must be served by a common deadline. Given that, for each user, the channel fade state determines the throughput per unit of energy expended, our objective is to minimize the overall expected energy consumption while satisfying the deadline constraint. We consider both a linear and a strictly convex rate-power curve and obtain optimal solutions, based on dynamic programming (DP), and tractable approximate heuristics in both cases. For the special non-fading channel case with convex rate-power curve, an optimal solution is obtained based on the shortest path formulation. In the case of a linear rate-power curve, our DP solution has a nice "threshold" form; while for the convex rate-power curve we are able to obtain a heuristic algorithm with comparable performance with that of the optimal scheduling scheme.

In this paper, we study the benefits of using tunable transceivers for reducing the required number of electronic ports in wavelength-division-multiplexing/time-division multiplexing optical networks. We show that such transceivers can be used to efficiently "groom" subwavelength traffic in the optical domain and so can significantly reduce the amount of terminal equipment needed compared with the fixed-tuned case. Formulations for this "tunable grooming" problem are provided, where the objective is to schedule transceivers so as to minimize the required number of ports needed for a given traffic demand. We establish a relationship between this problem and edge colorings of graphs which are determined by the offered traffic. Using this relationship, we show that, in general, this problem is NP-complete, but we are able to efficiently solve it for many cases of interest. When the number of wavelengths in the network is not limited, each node is shown to only require the minimum number of transceivers (i.e., no more transceivers than the amount of traffic that it generates). This holds regardless of the network topology or traffic pattern. When the number of wavelengths is limited, an analogous result is shown for both uniform and hub traffic in a ring. We then develop a heuristic algorithm for general traffic that uses nearly the minimum number of transceivers. In most cases, tunable transceivers are shown to reduce the number of ports per node by as much as 60%. We also consider the case where traffic can dynamically change among an allowable set of traffic demands. Tunability is again shown to significantly reduce the port requirement for a nonblocking ring, both with and without rearrangements.

We consider dynamic routing and power allocation for a wireless network with time-varying channels. The network consists of power constrained nodes that transmit over wireless links with adaptive transmission rates. Packets randomly enter the system at each node and wait in output queues to be transmitted through the network to their destinations. We establish the capacity region of all rate matrices (/spl lambda//sub ij/) that the system can stably support-where /spl lambda//sub ij/ represents the rate of traffic originating at node i and destined for node j. A joint routing and power allocation policy is developed that stabilizes the system and provides bounded average delay guarantees whenever the input rates are within this capacity region. Such performance holds for general arrival and channel state processes, even if these processes are unknown to the network controller. We then apply this control algorithm to an ad hoc wireless network, where channel variations are due to user mobility. Centralized and decentralized implementations are compared, and the stability region of the decentralized algorithm is shown to contain that of the mobile relay strategy developed by Grossglauser and Tse (2002).

In this correspondence, we develop fundamental convexity properties of unfinished work and packet waiting time in a queue serving general stochastic traffic. The queue input consists of an uncontrollable background process and a rate-controllable input stream. We show that any moment of unfinished work is a convex function of the controllable input rate. The convexity properties are then extended to address the problem of optimally routing arbitrary input streams over a collection of K queues in parallel with different (possibly time-varying) server rates (/spl mu//sub 1/(t),...,/spl mu//sub K/(t)). Our convexity results hold for stream-based routing (where individual packet streams must be routed to the same queue) as well as for packet-based routing where each packet is routed to a queue by probabilistic splitting. Our analysis uses a novel technique that combines sample path observations with stochastic equivalence relationships.

We consider the throughput/delay tradeoffs for scheduling data transmissions in a mobile ad hoc network. To reduce delays in the network, each user sends redundant packets along multiple paths to the destination. Assuming the network has a cell partitioned structure and users move according to a simplified independent and identically distributed (i.i.d.) mobility model, we compute the exact network capacity and the exact end-to-end queueing delay when no redundancy is used. The capacity-achieving algorithm is a modified version of the Grossglauser-Tse two-hop relay algorithm and provides O(N) delay (where N is the number of users). We then show that redundancy cannot increase capacity, but can significantly improve delay. The following necessary tradeoff is established: delay/rate/spl ges/O(N). Two protocols that use redundancy and operate near the boundary of this curve are developed, with delays of O(/spl radic/N) and O(log(N)), respectively. Networks with non-i.i.d. mobility are also considered and shown through simulation to closely match the performance of i.i.d. systems in the O(/spl radic/N) delay regime.

In this correspondence, we analyze feedforward tree networks of queues serving fixed-length packets. Using sample path conservation properties and stochastic coupling techniques, we analyze these systems without making any assumptions about the nature of the underlying input processes. In the case when the server rate is the same for all queues, the exact packet occupancy distribution in any queue of a multistage network is obtained in terms of a reduced two-stage equivalent model. Simple and exact expressions for occupancy mean and variance are derived from this result, and the network is shown to exhibit a natural traffic smoothing property, where preliminary stages act to smooth or improve traffic for downstream nodes. In the case of heterogeneous server rates, a similar type of smoothing is demonstrated, and upper bounds on the backlog distribution are derived. These bounds hold for general input streams and are tighter than currently known bounds for leaky bucket and stochastically bounded bursty traffic.

We consider the problem of wavelength assignment in reconfigurable WDM networks with wavelength converters. We show that for N-node P-port bidirectional rings, a minimum number of /spl lceil/PN/4/spl rceil/ wavelengths are required to support all possible connected virtual topologies in a rearrangeably nonblocking fashion, and provide an algorithm that meets this bound using no more than /spl lceil/PN/2/spl rceil/ wavelength converters. This improves over the tight lower bound of /spl lceil/PN/3/spl rceil/ wavelengths required for such rings given in if no wavelength conversion is available. We extend this to the general P-port case where each node i may have a different number of ports P/sub i/, and show that no more than /spl lceil//spl sigma//sub i/P/sub i//4/spl rceil/+1 wavelengths are required. We then provide a second algorithm that uses more wavelengths yet requires significantly fewer converters. We also develop a method that allows the wavelength converters to be arbitrarily located at any node in the ring. This gives significant flexibility in the design of the networks. For example, all /spl lceil/PN/2/spl rceil/ converters can be collocated at a single hub node, or distributed evenly among the N nodes with min{/spl lceil/P/2/spl rceil/+1,P} converters at each node.

We develop an on-line wavelength assignment (WA) algorithm for a wavelength-routed WDM tree network. The algorithm dynamically supports all k-port traffic matrices among N end nodes, where k denotes an integer vector [k/sub 1/...,k/sub N/] and end node i,1/spl les/i/spl les/N, can transmit at most k/sub i/ wavelengths and receive at most k/sub i/ wavelengths. Our algorithm is rearrangeably nonblocking, uses the minimum number of wavelengths, and requires at most d/sup */-1 lightpath rearrangements per new session request, where d/sup */ is the degree of the most heavily used node. We observe that the number of lightpath rearrangements per new session request does not increase as the amount of traffic k scales up by an integer factor. In addition, wavelength converters cannot reduce the number of wavelengths required to support k-port traffic in a tree network. We show how to implement our WA algorithm using a hybrid wavelength-routed/broadcast tree with only one switching node connecting several passive broadcast subtrees. Finally, using roughly twice the minimum number of wavelengths for a rearrangeably nonblocking WA algorithm, we can modify the WA algorithm to be strict-sense nonblocking.

This paper addresses the energy-efficient broadcasting problem in ad hoc wireless networks. First, we show that finding the minimum-energy broadcast tree is NP-complete. We then develop a distributed clustering algorithm that computes energy-efficient broadcast trees in polynomial time. Our distributed algorithm computes all N possible broadcast trees simultaneously, while requiring O(N/sup 2/) messages to be exchanged between nodes. We compare our algorithm's performance to the best-known centralized algorithm, and show that it constructs trees consuming, on average, only 18% more energy. We also consider the possibility of having multiple source nodes that can be used to broadcast the message and adapt our algorithm to compute energy-efficient broadcast trees with multiple source nodes. We observe a reduction in the amount of energy needed to form the broadcast tree that is linear in the number of source nodes.

We consider the throughput/delay tradeoffs for scheduling data transmissions in a mobile ad-hoc network. To reduce delays in the network, each user sends the redundant packets along multiple paths to the destination. Assuming the network has a cell partitioned structure and users move according to a simplified iid mobility model, we compute the exact network capacity and the exact end-to-end queueing delay when no redundancy is used. The capacity achieving algorithm is a modified version of the Grossglauser-Tse 2-hop relay algorithm and provides O(N) delay (where N is the number of users). We then show that redundancy cannot increase capacity, but can significantly improve delay. The following necessary tradeoff is established: delay/rate /spl ges/ O(N). Two protocols which use redundancy and operate near the boundary of this curve are developed, with delays of O(/spl radic/N) and O(log(N)), respectively. Networks with non-iid mobility are also considered and shown through simulation to closely match the performance of iid systems in the O(/spl radic/N) delay regime.

Switching traffic together in bundles of wavelengths called wavebands can greatly reduce the switching costs of the network. We consider the problem of partitioning wavelengths into wavebands for star networks using the minimum number of total wavebands. We provide a greedy algorithm for waveband partitioning and show that it is optimal in that it requires the minimum number of wavebands subject to using the minimum possible number of wavelengths. We also give an algorithm for allocating calls from any admissible traffic set to the wavebands in a non-blocking manner. Finally, we show that the increase in the number of wavebands required is logarithmic in the number of calls and polynomial in the size of the network.

We study the benefits of using tunable transceivers for reducing the required number of electronic ports in WDM/TDM networks. We show that such transceivers can be used to efficiently "groom" sub-wavelength traffic in the optical domain and so can significantly reduce the number of electronic ports compared to the fixed tuned case. We provide a new formulation for this "tunable grooming" problem. We show that in general this problem is NP-complete, but we are able to efficiently solve it for many cases of interest. When the number of wavelengths in the network is not limited, we show that each node only needs the minimum number of transceivers (i.e., no more transceivers than the amount of traffic that it generates). This holds regardless of the network topology or traffic pattern. When the number of wavelengths is limited, we show an analogous result for both uniform and hub traffic in a ring. We also develop a heuristic algorithm for general traffic that uses nearly the minimum number of transceivers. In most cases, tunable transceivers are shown to reduce the number of ports per node by as much as 60%.

This paper analyzes the performance of TCP over satellite links with random access. The system considered consists of large number of identical source-destination pairs, each employing TCP at its transport layer and a random access scheme at its MAC layer. Simple formulas that well capture the system performance are given, and some important properties of the system performance are presented as well. Specifically, in order to analyze the system and proposes a simplified version of the system. Then formulas were developed for obtaining the throughput of this simplified system as a function of various system and protocol parameters. Based on these formulas, it is shown that the maximum possible system throughput is 1/e, which can be achieved only when the system parameters satisfy a given condition. The optimal MAC layer transmission probability at which the throughput is maximized is derived as well. Furthermore, the impact of varying system and protocol parameters on the system performance is analyzed. The results show that for systems with very small propagation delay or very large number of source-destination pairs, a throughput of 1/e can be achieved by setting the MAC layer transmission probability to its optimal value. However, when the number of users is (relatively) small or the propagation delay is (relatively) large, the maximum achievable throughput can be substantially smaller than 1/e. Although the analysis is based on the simplified system, simulations on the original system show that the formulas and the above results can be used to describe the performance of the original system as well.

We consider the role of switching in minimizing the number of electronic ports [e.g., synchronous optical network (SONET) add/drop multiplexers] in an optical network that carries subwavelength traffic. Providing nodes with the ability to switch traffic between wavelengths, such as through the use of SONET cross-connects, can reduce the required number of electronic ports. We show that only limited switching ability is needed for significant reductions in the number of ports. First, we consider architectures where certain "hub" nodes can switch traffic between wavelengths and other nodes have no switching capability. For such architectures, we provide a lower bound on the number of electronic ports that is a function of the number of hub nodes. We show that our lower bound is relatively tight by providing routing and grooming algorithms that nearly achieve the bound. For uniform traffic, we show that the number of electronic ports is nearly minimized when the number of hub nodes used is equal to the number of wavelengths of traffic generated by each node. Next, we consider architectures where the switching ability is distributed throughout the network. Such architectures are shown to require a similar number of ports as the hub architectures, but with a significantly smaller "switching cost." We give an algorithm for designing such architectures and characterize a class of topologies, where the minimum number of ports is used. Finally, we provide a general upper bound on the amount of switching required in the network. For uniform traffic, our bound shows that as the size of the network increases, each traffic stream must be switched at most once in order to achieve the minimum port count.

In a wavelength-division multiplexed (WDM)-based network, a single physical link failure may correspond to multiple logical link failures. As a result, two-connected logical topologies, such as rings routed on a WDM physical topology, may become disconnected after a single physical link failure. We consider the design of physical topologies that ensure logical rings can be embedded in a survivable manner. This is of particular interest in metropolitan area networks, where logical rings are in practice almost exclusively employed for providing protection against link failures. First, we develop necessary conditions for the physical topology to be able to embed all logical rings in a survivable manner. We then use these conditions to provide tight bounds on the number of physical links that an N-node physical topology must have in order to support all logical rings for different sizes K. We show that when K/spl ges/4 the physical topology must have at least 4N/3 links, and that when K/spl ges/6 the physical topology must have at least 3N/2 links. Subsequently, we generalize this bound for all K/spl ges/4. When K/spl ges/N-2, we show that the physical topology must have at least 2N-4 links. Finally, we design physical topologies that meet the above bounds for both K=4 and K=N-2. Specifically, our physical topology for embedding (N-2)-node rings has a dual hub structure and is able to embed all rings of size less than N-1 in a survivable manner. We also provide a simple extension to this topology that addresses rings of size K=N-1 and rings of size K=N for N odd. We observe that designing the physical topology for supporting all logical rings in a survivable manner does not use significantly more physical links than a design that only supports a small number of logical rings. Hence, our approach of designing physical topologies that can be used to embed all possible ring logical topologies does not lead to a significant overdesign of the physical topology.

This paper develops routing and scheduling algorithms for packet transmission in a low Earth orbit satellite network with a limited number of transmitters and buffer space. We consider a packet switching satellite network, where time is slotted and the transmission time of each packet is fixed and equal to one time slot. Packets arrive at each satellite independently with a some probability during each time slot; their destination satellite is uniformly distributed. With a limited number of transmitters and buffer space on-board each satellite, contention for transmission inevitably occurs as multiple packets arrive at a satellite. First, we establish the stability region of the system in terms of the maximum admissible packet arrival rate that can possibly be supported. We then consider three transmission scheduling schemes for resolving these contentions: random packet win, where the winning packet is chosen at random; oldest packet win, where the packet that has traveled the longest distance wins the contention; and shortest hops win (SHW), where the packet closest to its destination wins the contention. We evaluate the performance of each of the schemes in terms of throughput. For a system without a buffer, the SHW scheme attains the highest throughput. However, when even limited buffer space is available, all three schemes achieve about the same throughput performance. Moreover, even with a buffer size of just a few packets the achieved throughput is close to that of the infinite buffer case.

In a WDM-based network, a single physical link failure may correspond to multiple logical link failures. As a result, 2-connected logical topologies, such as rings routed on a WDM physical topology, may become disconnected after a single physical link failure. We consider the design of physical topologies that ensure logical rings can be embedded in a survivable manner. First, we develop necessary conditions on the physical topology to be able to embed all logical rings in a survivable manner. We then use these conditions to provide lower bounds on the number of physical links that an TV-node physical topology must have in order to support all logical rings for even sizes K. For example, we show that when K /spl ges/ 4 the physical topology must have at least 4N/3 links, and that when K /spl ges/ 6 the physical topology must have at least 3N/2 links, and when K /spl ges/ 8 the physical topology must have at least 1.6N links. Furthermore, we show that for K /spl ges/ N - 2 the physical topology must have at least 2N - 4 links. Finally, we design a physical topology that meets the above bound for K = N - 2. We then modify this physical topology to embed rings of size K = N - 1 and K = N.

We consider the problem of wavelength assignment in a reconfigurable bidirectional ring network with wavelength converters. We show that for N-node P-port bidirectional rings, a minimum number of /spl lceil/PN/4/spl rceil/ wavelengths are required to support all possible virtual topologies in a rearrangeably nonblocking fashion, and provide an algorithm that meets this bound for connected topologies using no more than /spl lceil/PN/2/spl rceil/ wavelength converters. This improves over the tight lower bound of /spl lfloor/PN/3/spl rfloor/ wavelengths required for such rings given in A. Narula-Tam et al. (2002)] if no wavelength conversion is available. We also provide another algorithm that uses more wavelengths yet requires significantly fewer converters. Both algorithms are then extended to the case of unconnected topologies using at most one additional wavelength. Finally, we develop a method that allows the wavelength converters to be arbitrarily located at any node in the ring. This gives significant flexibility in the design of the networks. For example, all /spl lceil/PN/2/spl rceil/ converters can be collocated at a single hub node, or distributed evenly among the N nodes with /spl lceil/P/2 /spl rceil/ converters at each node.

We seek to maximize the data throughput of an energy and time constrained transmitter sending data over a fading channel. The transmitter has a fixed amount of energy and a limited amount of time to send data. Given that the channel fade state determines the throughput obtained per unit of energy expended, the goal is to obtain a policy for scheduling transmissions that maximizes the expected data throughput. We develop a dynamic programming formulation that leads to an optimal closed-form transmission schedule. We then extend our approach to the problem of minimizing the energy required to send a fixed amount of data over a fading channel given deadline constraints.

We consider dynamic routing and power allocation for a wireless network with time varying channels. The network consists of power constrained nodes which transmit over wireless links with adaptive transmission rates. Packets randomly enter the system at each node and wait in output queues to be transmitted through the network to their destinations. We establish the capacity region of all rate matrices (/spl lambda//sub ij/) that the system can stably support - where (/spl lambda//sub ij/) represents the rate of traffic originating at node i and destined for node j. A joint routing and power allocation policy is developed which stabilizes the system and provides bounded average delay guarantees whenever the input rates are within this capacity region. Such performance holds for general arrival and channel state processes, even if these processes are unknown to the network controller. We then apply this control algorithm to an ad-hoc wireless network where channel variations are due to user mobility, and compare its performance with the Grossglauser-Tse (2001) relay model.

We develop on-line routing and wavelength assignment (RWA) algorithms for WDM bidirectional ring and torus networks with N nodes. The algorithms dynamically support all k-allowable traffic matrices, where k denotes an arbitrary integer vector [k/sub 1/, k /sub 2/, ..., k/sub N/], and node i, 1/spl les/i/spl les/N, can transmit at most k/sub i/ wavelengths and receive at most k/sub i/ wavelengths. Both algorithms support the changing traffic in a rearrangeably nonblocking fashion. Our first algorithm, for a bidirectional ring, uses /spl lceil/(/spl Sigma//sub i=1//sup N/k/sub i/)/3/spl rceil/ wavelengths in each ring direction and requires at most three lightpath rearrangements per new session request regardless of the number of nodes N and the amount of traffic k. When all the k/sub i/s are equal to k, the algorithm uses /spl lceil/kN/3/spl rceil/ wavelengths, which is known to be the minimum for any off-line rearrangeably nonblocking algorithm. Our second algorithm, for a torus topology, is designed for the special case with all the k/sub i/s equal to k. For a square torus network with N nodes, the algorithm uses /spl lceil/k/spl radic/N/2/spl rceil/ wavelengths in each fiber, which is shown to be at most two times a lower bound obtained by assuming full wavelength conversion at all nodes. In addition, the algorithm requires at most /spl radic/N-1 lightpath rearrangements per new session request regardless of the amount of traffic k.

We develop algorithms for finding minimum energy disjoint paths in an all-wireless network, for both the node and link-disjoint cases. Our major results include a novel polynomial time algorithm that optimally solves the minimum energy 2 link-disjoint paths problem, as well as a polynomial time algorithm for the minimum energy k node-disjoint paths problem. In addition, we present efficient heuristic algorithms for both problems. Our results show that link-disjoint paths consume substantially less energy than node-disjoint paths. We also found that the incremental energy of additional link-disjoint paths is decreasing. This finding is somewhat surprising due to the fact that in general networks additional paths are typically longer than the shortest path. However, in a wireless network, additional paths can be obtained at lower energy due to the broadcast nature of the wireless medium. Finally, we discuss issues regarding distributed implementation and present distributed versions of the optimal centralized algorithms presented in the paper.

We address the issue of optimal energy allocation and admission control for communications satellites in Earth orbit. Such satellites receive requests for transmission as they orbit the Earth, but may not be able to serve them all, due to energy limitations. The objective is to choose which requests to serve so that the expected total reward is maximized. The special case of a single energy-constrained satellite is considered. Rewards and demands from users for transmission (energy) are random and known only at request time. Using a dynamic programming approach, an optimal policy is derived and is characterized in terms of thresholds. Furthermore, in the special case where demand for energy is unlimited, an optimal policy is obtained in closed form. Although motivated by satellite communications, our approach is general and can be used to solve a variety of resource allocation problems in wireless communications.

We consider power and server allocation in a multibeam satellite downlink which transmits data to N different ground locations over N time-varying channels. Packets destined for each ground location are stored in separate queues and the server rate for each queue, i, depends on the power, p/sub i/(t), allocated to that server and the channel state, c/sub i/(t), according to a concave rate-power curve /spl mu//sub i/(p/sub i/,c/sub i/). We establish the capacity region of all arrival rate vectors (/spl lambda//sub 1/,...,/spl lambda//sub N/) which admit a stabilizable system. We then develop a power-allocation policy which stabilizes the system whenever the rate vector lies within the capacity region. Such stability is guaranteed even if the channel model and the specific arrival rates are unknown. Furthermore, the algorithm is shown to be robust to arbitrary variations in the input rates and a bound on average delay is established. As a special case, this analysis verifies stability and provides a performance bound for the choose-the-K-largest-connected-queues policy when channels can be in one of two states (ON or OFF ) and K servers are allocated at every timestep (K

We address the issue of optimal energy allocation and admission control for communications satellites in Earth orbit. These satellites receive requests for transmission as they orbit the Earth, but may not be able to serve them all, due to energy limitations. The objective is to choose which requests to serve so that the expected total reward is maximized. The special case of a single energy-constrained satellite is considered. Rewards and demands from users for transmission (energy) are random and known only at request time. Using a dynamic programming approach, an optimal policy is derived and is characterized in terms of thresholds. Furthermore, in the special case where demand for energy is unlimited, an optimal policy is obtained in dosed form. Although motivated by satellite communications, our approach is general and can be used to solve a variety of resource allocation problems in wireless communications.

We consider power and server allocation in a multi-beam satellite downlink which transmits data to N different ground locations over N time-varying channels. Packets destined for each ground location are stored in separate queues, and the server rate for each queue i depends on the power p/sub i/(t) allocated to that server and the channel state c/sub i/(t) according to a concave rate-power curve /spl mu//sub i/(p/sub i/, c/sub i/). We establish the capacity region of all arrival rate vectors which admit a stabilizable system. For the case when channel states and arrivals are iid from timeslot to timeslot, we develop a particular power allocation policy which stabilizes the system whenever the rate vector lies within the capacity region. Such stability is guaranteed even if the channel model and the specific arrival rates are unknown. As a special case, this analysis verifies the stability of the "choose-the-K-largest-connected-queues" policy when channels can be in one of two states (ON or OFF) and K servers are allocated at every timestep (K

This paper considers the link capacity requirement for a N/spl times/N mesh-torus network under a uniform all-to-all traffic model. Both primary capacity and spare capacity for recovering from link failures are examined. In both cases, we use a novel method of "cuts on a graph" to obtain lower bounds on capacity requirements and subsequently find algorithms for routing and failure recovery that meet these bounds. Finally, we quantify the benefits of path based restoration over that of link based restoration; specifically, we find that the spare capacity requirement for a link based restoration scheme is nearly N times that for a path based scheme.

We propose a new protection scheme, which we term partial path protection (PPP), to select end-to-end backup paths using local information about network failures. PPP designates a different restoration path for every link failure on each primary path. PPP also allows reuse of operational segments of the original primary path in the protection path. A novel approach used in this paper is that of a dynamic call-by-call model with blocking probability as the performance metric, this model is in contrast with traditional capacity-efficiency measurement for batch call arrivals. Additionally, we show that a simple method based on shortest path routing for which primary paths are selected first is more effective than a greedy approach that minimizes, for each call arrival, the number of wavelengths used by the primary and backup path jointly.

Network restoration is often done at the electronic layer by rerouting traffic along a redundant path. With wavelength-division multiplexing (WDM) as the underlying physical layer, it is possible that both the primary and backup paths traverse the same physical links and would fail simultaneously in the event of a link failure. It is, therefore, critical that lightpaths are routed in such a way that a single link failure would not disconnect the network. We call such a routing survivable and develop algorithms for survivable routing of a logical topology. First, we show that the survivable routing problem is NP-complete. We then prove necessary and sufficient conditions for a routing to be survivable and use these conditions to formulate the problem as an integer linear program (ILP). Due to the excessive run-times of the ILP, we develop simple and effective relaxations for the ILP that significantly reduces the time required for finding survivable routings. We use our new formulation to route various logical topologies over a number of different physical topologies and show that this new approach offers a much greater degree of protection than alternative routing schemes such as shortest path routing and a greedy routing algorithm. Finally, we consider the special case of ring logical topologies for which we are able to find a significantly simplified formulation. We establish conditions on the physical topology for routing logical rings in a survivable manner.

Through the use of configurable wavelength-division-multiplexing (WDM) technology including tunable optical transceivers and frequency selective switches, next-generation WDM networks will allow multiple virtual topologies to be dynamically established on a given physical topology. For N node P port networks, we determine the number of wavelengths required to support all possible virtual topologies (PN lightpaths) on a bidirectional ring physical topology. We show that if shortest path routing is used, approximately N wavelengths are needed to map N lightpaths. We then present novel adaptive lightpath routing and wavelength assignment strategies that reduce the wavelength requirements to [(N/2)] working wavelengths per port for protected networks and [(N/3)] wavelengths in each direction per port for unprotected networks. We show that this reduced wavelength requirement is optimal in the sense that it is the minimum required to support the worst case logical topology. Furthermore, we prove that a significant number of logical topologies require this minimum number of wavelengths. We also develop joint routing and wavelength assignment strategies that not only minimize the number of wavelengths required to implement the worst case logical topologies but also reduce average wavelength requirements. Finally, methods for extending these routing and wavelength assignment results to general two-connected and three-connected physical topologies are presented.

Network restoration is often done at the electronic layer by rerouting traffic along a redundant path. With wavelength division multiplexing (WDM) as the underlying physical layer, it is possible that both the primary and backup paths traverse the same physical links and would fail simultaneously in the event of a link failure. It is therefore critical that lightpaths are routed in such a way that a single link failure would not disconnect the network. We call such a routing survivable and develop algorithms for survivable routing of a logical topology. We prove necessary and sufficient conditions for a routing to be survivable and use this condition to formulate the problem as an integer linear program. We use our new formulation to route various logical topologies over a number of different physical topologies and show that this new approach offers a much greater degree of protection than alternative routing schemes such as shortest path routing and a greedy routing algorithm.

In this paper we develop fundamental convexity properties of unfinished work and packet waiting time in a work conserving */*/1 queue. The queue input consists of an uncontrollable background process and a rate-controllable input stream. We show that any moment of unfinished work is a convex function of the controllable input rate. The convexity properties are then extended to address the problem of optimal routing of arbitrary input streams over a collection of N queues in parallel with different (possibly time-varying) linespeeds (/spl mu//sub 1/(t),..., /spl mu//sub N/(t)). Our convexity results hold for stream-based routing (where individual packet streams must be routed to the same queue) as well as for packet-based routing where each packet is routed to a queue using some pre-determined splitting method, such as probabilistic splitting. Our analysis of these general systems is carried out by introducing a new function of the superposition of two input streams that we call the blocking function. Using this function facilitates analysis and provides much insight into the sample path dynamics of */*/1 queues.

Through the use of configurable WDM technology including tunable optical transceivers and frequency selective switches, next generation WDM networks will allow multiple virtual topologies to be dynamically established on a given physical topology. We determine the number of wavelengths required to support all possible virtual topologies on a bidirectional ring physical topology. We first determine wavelength requirements for networks using shortest path routing. We then reduce network wavelength requirements by presenting novel adaptive lightpath routing and wavelength assignment strategies. We also show that this reduced wavelength requirement is optimal. These results are first derived for the single port per node case and then extended to networks with multiple ports per node.

We develop load balancing algorithms for WDM-based packet networks in which the average traffic between nodes is dynamically changing. In WDM-based packet networks, routers are connected to each other using wavelengths (lightpaths) to form a logical network topology. This logical topology may be reconfigured by rearranging the lightpaths connecting the routers. The goal of our load balancing algorithms is to minimize network delay by reconfiguring the logical topology. Since delay becomes unbounded as the load approaches the link capacity, delay is usually dominated by the most heavily loaded link. Therefore, our algorithms attempt to minimize the maximum link load. Even when traffic is static, deriving the optimal logical topology for a given traffic pattern is known to be NP-complete. Previous work on reconfiguration proposed heuristic algorithms to determine the "best" logical topology for the given traffic pattern and migrated to that topology using a series of reconfiguration steps. However, when traffic patterns are changing rapidly, reconfiguring the full network with every change in the traffic may be extremely disruptive. In this paper, we develop iterative reconfiguration algorithms for load balancing that track rapid changes in the traffic pattern. At each reconfiguration step, our algorithms make only a small change to the network topology, hence, minimizing the disruption to the network. We study the performance of our algorithms under several dynamic traffic scenarios and show that our algorithms perform near optimally.

We attempt to characterize the gain in traffic capacity that a reconfigurable network offers over a fixed topology network. We define the gain as the ratio of the maximum offered loads that the two systems can support for a given blocking probability. We develop a system model to analytically predict the blocking probability for both the fixed and reconfigurable systems. This model is different from previous models developed to analyze the blocking probability in WDM networks in that it accounts for a port limitation at the nodes. We study high-bandwidth calls, where each call requires an entire wavelength. We find that reconfigurability offers a substantial performance improvement, particularly when the number of available wavelengths significantly exceeds the number of ports per node. In this case, we find that the gain approaches a factor of N/2 over a fixed topology unidirectional ring, and N/4 over a fixed topology bi-directional ring (where N is the number of nodes in the ring). We validate our model via simulation, and we find that it agrees strongly with the simulation results, particularly for a large number of ports per node. We also obtain upper and lower bounds on capacity for various ring topologies that give additional insight into the benefits of configurability.

This paper is about the design and quantitative analysis of distributed approaches for optical flow switching (using dynamic lightpath setup) in a wide area WDM backbone network. The major contribution of this work is to design realistic integrated approaches for flow routing, wavelength assignment, and connection setup in a truly distributed setting, and assess the relative performance of these on a nationwide wide area network (WAN) backbone. A simulation model is used which models timing, wavelength, and fiber constraints. Results are presented in terms of backbone utilization for a given blocking probability of optical flows.

In this paper, we consider traffic grooming in WDM/SONET ring networks when the offered traffic is characterized by a set of traffic matrices. Our objective is to minimize the cost of electronic add/drop multiplexers (ADMs) in the network, while being able to support any offered traffic matrix in a rearrangeably nonblocking manner. We provide several methods for reducing the required number of ADMs for an arbitrary class of traffic matrices. We then consider the special case where the only restriction on the offered traffic is a constraint on the number of circuits a node may source at any given time. For this case, we provide a lower bound on the number of ADMs required and give conditions that a network must satisfy in order for it to support the desired set of traffic patterns. Circuit assignment and ADM placement algorithms with performance close to this lower bound are provided. These algorithms are shown to reduce the electronic costs of a network by up to 27%. Finally, we discuss extensions of this work for supporting dynamic traffic in a wide-sense or strict sense nonblocking manner as well as the benefits of using a hub node and tunable transceivers. Much of this work relies on showing that these grooming problems can often be formulated as standard combinatorial optimization problems.

We develop load balancing algorithms for WDM-based packet networks where the average traffic between nodes is dynamically changing. In WDM-based packet networks, routers are connected to each other using wavelengths (lightpaths) to form a logical network topology. The logical topology may be reconfigured by rearranging the lightpaths connecting the routers. Our algorithms reconfigure the logical topology to minimize the maximum link load. In this paper, we develop iterative reconfiguration algorithms for load balancing that track rapid changes in the traffic pattern. At each reconfiguration step, our algorithms make only a small change to the network topology hence minimizing the disruption to the network. We study the performance of our algorithms under several dynamic traffic scenarios and show that our algorithms perform near optimally. We further show that these large reconfiguration gains are achievable in systems with a limited number of wavelengths.

In this paper we consider the circuit assignment algorithm for dynamic traffic in unidirectional WDM/SONET ring networks. Our objective is to minimize the cost of electronic add/drop multiplexers (ADMs) in the network, while being able to support any offered traffic matrix in a rearrangeably non-blocking manner. The only restriction on the offered traffic is a constraint on the number of circuits a node may source at any given time. We provide a lower bound on the number of ADMs required and give conditions that a network must satisfy in order for it to support the desired set of traffic patterns. Circuit assignment and ADM placement algorithms that perform closely to this lower bound are provided. These algorithms are shown to reduce the electronic costs of a network by over 30%. Finally, we discuss extensions of this work for supporting dynamic traffic in a wide-sense or strict sense non-blocking manner as well as the benefits of using a hub node and tunable transceivers.

We describe an architecture and medium access control (MAC) protocol for WDM networks. The system is based on a broadcast star architecture and uses an unslotted access protocol and a centralized scheduler to efficiently provide bandwidth-on-demand in WDM networks. To overcome the effects of propagation delays the scheduler measures the delays between the terminals and the hub and takes that delay into account when scheduling transmissions. Simple scheduling algorithms, based on a look-ahead capability, are used to overcome the effects of head-of-line blocking. An important application area for this system is in optical access networks, where this novel MAC protocol can be used to access wavelengths in a WDM passive optical network (PON).

We develop and analyze simple algorithms for scheduling multicast traffic in wavelength division multiplexing (WDM) broadcast-and-select networks with N nodes, W wavelengths, and a single receiver per node that can be tuned to any of the W wavelengths. Each message is addressed to /spl kappa/ randomly chosen nodes. Since optimal message scheduling in a WDM network is known to be very difficult, we study two simple scheduling schemes: in the first, a message is continuously retransmitted until it is received by all of its intended recipients; and in the second, a random delay is introduced between retransmissions of the same message. We develop a throughput analysis for both schemes using methods from discrete-time queueing systems and show that the algorithm with random delays between retransmissions results in higher throughput. We also consider a number of receiver algorithms for selecting among multiple simultaneous transmissions and show, through simulation, that an algorithm where the receiver selects the message with the least number of intended recipients performs better than a random selection algorithm. Finally, we show that channel utilization can be significantly increased with multiple receivers/node.

This paper considers the problem of scheduling multicast transmissions in a WDM broadcast based local area network. In very high speed networks optimal scheduling may be too time consuming and complex to be executed in real time, thus we are led to consider unscheduled (random) multicast transmissions. We consider two random scheduling schemes: in the first, a message is continuously retransmitted until it is received by all of its intended recipients; and in the second, a random delay is introduced between retransmissions of the same message. We develop an exact throughput analysis for both schemes using methods from discrete-time queueing systems and show that the algorithm with random delays between retransmissions results in higher throughput. Finally, we consider a number of receiver algorithms for selecting among multiple simultaneous transmissions and show that an algorithm where the receiver selects the message with the least number of intended recipients performs better than a random selection algorithm.

This paper describes two algorithms for scheduling packets in a multi-hop network. The objective of the algorithms is to reduce end-to-end message (not packet) transmission delays. Both algorithms schedule packet transmissions based on the length of the original message that the packet belongs to. The first algorithm is preemptive and is based on the shortest-message-first principle and the second is based on the shortest-remaining-transmit-time principle. We develop simulation models for analyzing the algorithms. The simulations show that when message sizes vary widely, these algorithms can significantly reduce average end-to-end message delays compared to first-come-first-serve scheduling.

We develop an approach to the analysis of average queueing delay in a tree network of discrete-time queues with constant service time. The analysis of such systems is pertinent to packet-switched data networks with fixed-length packets. Our solution is based on considering an equivalent network, in which at each node packets in transit are given priority over exogenous arrivals. The solution to the equivalent model is easily computed, and, hence, the solution to the original model can be obtained.

A common task for network protocols is the broadcasting of information from one node to the rest of the nodes in the network. This task is often required during the execution of parallel algorithms in a network of processors, or other situations where the nodes of a mesh network generate packets to be broadcast at random time instances. We consider processors communicating over a mesh network with the objective of broadcasting information among each other. One instance of the problem involves a number of nodes all with the same message to be broadcasted. For that problem, a lower-bound on the time to complete the broadcast, and an algorithm which achieves this bound are presented. In another instance, every node in the mesh has packets to be broadcast arriving independently, according to a Poisson random process. The stability region for performing such broadcasts is characterized, and broadcast algorithms which operate efficiently within that region are presented. These algorithms involve interacting queues whose analysis is known to be very difficult. Toward that end we develop an approximation which models an n-dimensional infinite Markov chain as a single-dimensional infinite Markov chain together with an n-dimensional finite Markov chain. This approximate model can be analyzed and the results compare favorably with simulation.

We present a packet multiple access protocol that is a hybrid of a pure CDMA protocol and an ALOHA random access protocol. The protocol utilizes the multireception capabilities of spread-spectrum communications together with the "statistical-multiplexing" capabilities of random access. We begin by presenting a multi-receiver random access protocol and analyze its throughput characteristics. We then develop collision resolution algorithms for the protocol that attempt to optimize its performance. These algorithms are analyzed through the use of simulation. We show that with proper choice of protocol parameters our protocol can handle all admissible traffic loads. We then propose a dynamic, adaptive extension to the protocol that uses limited feedback information to allow the protocol to vary its parameters based on the traffic load in the system. This dynamic, adaptive version of the protocol allows it to operate efficiently under a wide variety of traffic load conditions. At very light load conditions the protocol behaves as a pure random access protocol and at very high load it behaves as a pure fixed assignments protocol. Our protocol seems to be a good choice for providing random access on a satellite channel where propagation delays are long. It is also a natural choice for wireless transmission of very short (e.g., ATM) packets.

An approximate model for analyzing interacting queues is developed. This approximation models an N-dimensional infinite Markov chain by means of two Markov chains, one being one-dimensional and infinite and the other being N-dimensional and finite. The transition probabilities of each chain are expressed in terms of statistics of the other chain. The two chains are solved together iteratively to yield an approximation to the original N-dimensional infinite chain. The model is used to analyze systems of dependent queues which often arise in multiple access protocols. It is shown how this model can be used to analyze the ALOHA multiple access protocol as well as a previously proposed broadcast algorithm for a mesh network. The results compare very well with simulation.>

A simple model of distributed computation that requires information exchange over a noisy channel is considered. A communication protocol is utilized that requires alternate bit exchanges between two processors. First, the case of a single public channel is considered and the number of bits that need to be exchanged between the processors to permit delta -accuracy in their goal is compared. For this computation, an error-detection-and-retransmission mechanism of error control and an error-correction-and-retransmission mixture that are consistent with the logical protocol that governs this exchange are considered. Second, the case of the availability of an additional secret channel is considered and interest in determining the minimum number of bits that need to be exchanged over a secret channel in order to maintain in -uncertainty about the computation for an eavesdropper on the public channel is shown. Various subcases under this case are considered and an upper bound on the number of secret bits when no error-control scheme is used is obtained.>