A quantum switch is one of the most fundamental network elements for connecting different quantum devices. In this paper, we explore the “optimal entanglement policy” of a quantum switch under a scenario where the stored and entangled qubits in the quantum switch may undergo a decoherence process. Finding an optimal entanglement policy is important as it enables a quantum switch to make a judicious basis measurement based on the number of existing link-level entanglements to maximize the “weighted throughput”. We use a Markov decision process framework to model the dynamics of the quantum switch, and theoretically reveal a threshold-based relationship between bipartite and tripartite policies under a very general class of weight functions with a weight parameter β. We further extend our analysis to uncover athreshold-based structure of optimal policies. In particular, the optimal policy for the quantum switch is a bipartite or tripartite policy when β is below a threshold β∗Bor above a threshold β∗T, respectively. When β∗B∗T, the optimal policy becomes a “threshold-based and state-dependent entanglement policy”. We also extend the work to allow a mixture of bipartite and tripartite policies by introducing a state-dependent mixed action. We theoretically show threshold-related relationships between mixed and bipartite/tripartite policies. Moreover, we extend this analysis to study optimal policies and characterize the threshold-based structure when the mixed action is considered. We carry out extensive numerical experiments to confirm that the optimal entanglement policy has such structural property when the mixed action is considered or not.

Transfer learning leverages existing models to help train new models, rather than training the new models from scratch. Unfortunately, realizing transfer learning in distributed cloud-edge networks faces critical challenges such as online training, uncertain network environments, time-coupled control decisions, and the balance between resource consumption and model accuracy. In this paper, targeting classification tasks, we study the settings of both homogeneous and heterogeneous transfer learning in cloud-edge networks via orchestrating model placement, data dispatching, and inference aggregation. We formulate non-linear mixed-integer programs of long-term cost optimization over consecutive time slots, and design polynomial-time online algorithms by exploiting the real-time trade-off between preserving previous control decisions and applying new control decisions. Our approaches produce new models by combining the existing pre-trained offline models and the online models that are continuously updated based on the inference results of data samples arriving in streams. We rigorously prove that our approaches only incur the number of inference mistakes no greater than a constant times that of the single best model in hindsight, and achieve constant competitive ratios for the total cost. Evaluations have confirmed the superior performance of our approaches compared to other state-of-the-art methods upon real-world data traces, under text classification transfer learning tasks.

We study how to schedule data sources in a wireless time-sensitive information system with multiple heterogeneous and unreliable channels to minimize the total expected Age-of-Information (AoI). Although one could formulate this problem as a discrete-time Markov Decision Process (MDP), such an approach suffers from the curse of dimensionality and lack of insights. For single-channel systems, prior studies have developed lower-complexity solutions based on the Whittle index. However, Whittle index has not been studied for systems with multiple heterogeneous channels, mainly because indexability is not well defined when there are multiple dual cost values, one for each channel. To overcome this difficulty, we introduce new notions of partial indexability and partial index, which are defined with respect to one channel’s cost, given all other channels’ costs. We then combine the ideas of partial indices and max-weight matching to develop a Sum Weighted Index Matching (SWIM) policy, which iteratively updates the dual costs and partial indices. The proposed policy is shown to be asymptotically optimal in minimizing the total expected AoI, under a technical condition on a global attractor property. We also propose an interpolation-based algorithm to quickly compute (approximate) partial indices in real time. Extensive performance simulations demonstrate that the proposed policy offers significant gains over conventional approaches by achieving a near-optimal AoI. Further, the notion of partial index is of independent interest and could be useful for other problems with multiple heterogeneous resources.

In this work, we design quantum algorithms that are more efficient than classical algorithms to solve time-dependent and finite-horizon Markov Decision Processes (MDPs) in two distinct settings: (1) In the exact dynamics setting, where the agent has full knowledge of the environment’s dynamics (i.e., transition probabilities), we prove that our Quantum Value Iteration (QVI) algorithm QVI-1 achieves a quadratic speedup in the size of the action space $(A)$ compared with the classical value iteration algorithm for computing the optimal policy ($\pi^{\ast}$) and the optimal V-value function ($V_{0}^{\ast}$). Furthermore, our algorithm QVI-2 provides an additional speedup in the size of the state space $(S)$ when obtaining near-optimal policies and V-value functions. Both QVI-1 and QVI-2 achieve quantum query complexities that provably improve upon classical lower bounds, particularly in their dependences on $S$ and $A$. (2) In the generative model setting, where samples from the environment are accessible in quantum superposition, we prove that our algorithms QVI-3 and QVI-4 achieve improvements in sample complexity over the state-of-the-art (SOTA) classical algorithm in terms of $A$, estimation error $(\epsilon)$, and time horizon $(H)$. More importantly, we prove quantum lower bounds to show that QVI-3 and QVI-4 are asymptotically optimal, up to logarithmic factors, assuming a constant time horizon.

Motivated by edge computing with artificial intelligence, in this paper we study an adversarial bandit-learning problem with switching costs. Existing results in the literature either incur$\Theta(T^{\frac{2}{3}})$regret with bandit feedback, or rely on free full-feedback in order to reduce the regret to$O(\sqrt{T})$. In contrast, we expand our study to incorporate two new factors. First, full feedback could incur a cost. Second, the player may choose$2$(or more) arms at a time and observe their feedback, even though switching costs are still incurred when she changes the set of chosen arms. For the setting where the player pulls only one arm at a time, our new regret lower-bound shows that, even when costly full-feedback is added, the$\Theta(T^{\frac{2}{3}})$regret still cannot be improved. However, the dependence on the number of arms may be improved when the full-feedback cost is small. In contrast, for the setting where the player can choose$2$(or more) arms at a time, we provide a novel online learning algorithm that achieves a significantly lower regret equal to$O(\sqrt{T})$. Further, our new algorithm does not need any full feedback at all. This sharp difference therefore reveals the surprising power of choosing$2$(or more) arms for this type of bandit learning problems with switching costs. Both our new algorithm and regret analysis involve several new ideas in choosing the primary and secondary arms, tuning the weight-decay parameters within and across episodes, and using the loss differences in the weight updates, which may be of independent interest.

While ensemble methods can tackle concept drifts, obtaining pretrained models and conducting ensemble learning upon streamed data impose fundamental challenges, including the dynamic balance between system overhead and inference accuracy in uncertain system environments, and the interlacement between desired economic properties and long-term participation. In this paper, we propose the joint optimization which enables service providers to obtain models via repetitive auctions from the model providers and conduct ensemble methods online in a cost-efficient manner. We design polynomial-time online algorithms to solve the underlying non-linear mixed-integer social cost minimization problem, involving bid selection, payment allocation, model hosting, and ensemble model-weight adaption. We further rigorously prove the performance guarantees with our approach, such as the sub-linear dynamic regret for the bidding cost, the sub-linear dynamic fit for the long-term participation constraint, the truthfulness and the individual rationality for the auctions, the upper bound for ensemble inference loss, and the parameterized-constant competitive ratio for the long-term social cost. Through extensive trace-driven evaluations under real-world settings, we have validated the significant advantages of our approach over multiple baselines and state-of-the-art algorithms.

Reactive power injection of distributed energy resources (DERs) can be used to mitigate the voltage disruption caused by the power injection from renewable generation. However, how to control the amount of reactive power injection in the presence of both adversary and uncertain renewable-generation and load remains a challenging problem. In this paper, we formulate a robust optimization problem for solving the setpoint controlling the reactive power injection of DER devices, so that the maximum potential voltage disruption across a feeder caused by uncertain environment and adversary is minimized. Our formulation is general and can be applied to both an adaptive setpoint method (where the VAR injection is a function of the renewable generation) and a static setpoint method (where the VAR injection is a fixed). While this problem incurs exponential complexity, we develop a fast approximate solution. Our numerical results demonstrate that the adaptive method can maintain the voltage disruption to be within a small neighborhood of the nominal voltage over a larger set of uncertainty than the static setpoint method.

We study a scheduling problem for a base-station transmitting status information to multiple user-equipments (UE) with the goal of minimizing the total expected Age-of-Information (AoI). Such a problem can be formulated as a Restless Multi-Armed Bandit (RMAB) problem and solved asymptotically-optimally by a low-complexity Whittle index policy, if each UE’s sub-problem is Whittle indexable. However, proving Whittle indexability can be highly non-trivial, especially when the value function cannot be derived in closed-form. In particular, this is the case for the AoI minimization problem with stochastic arrivals and unreliable channels, whose Whittle indexability remains an open problem. To overcome this difficulty, we develop a sufficient condition for Whittle indexability based on the notion of active time (AT). Even though the AT condition shares considerable similarity to the Partial Conservation Law (PCL) condition, it is much easier to understand and verify. We then apply our AT condition to the stochastic-arrival unreliable-channel AoI minimization problem and, for the first time in the literature, prove its Whittle indexability. Our proof uses a novel coupling approach to verify the AT condition, which may also be of independent interest to other large-scale RMAB problems.

Motivated by an Age-of-Information (AoI) minimization problem for systems with both fast (but unreliable) and slow (but more reliable) channels, in this paper we are interested in MDPs (Markov Decision Processes) where multiple agents compete for multiple heterogeneous channels. Such an MDP is known to suffer the curse-of-dimensionality when the number of sources is large. Recently, a partial index approach, which generalizes the Whittle index for single-channel systems, has been proposed to decompose such a large-scale MDP into smaller sub-problems, if each sub-problem satisfies the partial indexability and the precise division property. Unfortunately, verifying partial indexability and the precise division property is highly non-trivial. This paper provides a new Active-Time (AT) condition, which ensures the precise-division property (which then implies the partial indexability). Our new AT condition generalizes the AT condition for Whittle indexability in a non-trivial manner, and is much easier to verify for systems with heterogeneous channels. We then apply our AT condition to the fast-slow-channel setting, and establish its partial indexability for the first time in the literature. Our analysis reveals new semi-threshold structures of the optimal policy, and uses a new coupling approach to analyze the corresponding AT condition, which could also be of independent interest. Numerical simulations are provided to verify our theoretical results and to demonstrate the close-to-optimal performance of the partial index policy.

There has been significant interest in leveraging limited look-ahead to achieve low competitive ratios for online convex optimization (OCO). However, existing online algorithms (such as Averaging Fixed Horizon Control (AFHC)) that can leverage look-ahead to reduce the competitive ratios still produce competitive ratios that grow unbounded as the coefficient ratio (i.e., the maximum ratio of the switching-cost coefficient and the service-cost coefficient) increases. On the other hand, the regularization method can attain a competitive ratio that remains bounded when the coefficient ratio is large, but it does not benefit from look-ahead. In this paper, we propose a new algorithm, called Regularization with Look-Ahead (), that can get the best of both AFHC and the regularization method, i.e., its competitive ratio decreases with the look-ahead window size when the coefficient ratio is small, and remains bounded when the coefficient ratio is large. Moreover, we provide a matching lower bound for the competitive ratios of all online algorithms with look-ahead, which differs from the achievable competitive ratio of within a factor that only depends on the problem size. Further, the competitive analysis of involves a non-trivial generalization of online primal-dual analysis to the case with look-ahead.

There is a growing interest in designing Graph Neural Networks (GNNs) for seeded graph matching, which aims to match two unlabeled graphs using only topological information and a small set of seed nodes. However, most previous GNNs for this task use a semi-supervised approach, which requires a large number of seeds and cannot learn knowledge that is transferable to unseen graphs. In contrast, this paper proposes a new supervised approach that can learn from a training set how to match unseen graphs with only a few seeds. Our SeedGNN architecture incorporates several novel designs, inspired by theoretical studies of seeded graph matching: 1) it can learn to compute and use witness-like information from different hops, in a way that can be generalized to graphs of different sizes; 2) it can use easily-matched node-pairs as new seeds to improve the matching in subsequent layers. We evaluate SeedGNN on synthetic and real-world graphs and demonstrate significant performance improvements over both non-learning and learning algorithms in the existing literature. Furthermore, our experiments confirm that the knowledge learned by SeedGNN from training graphs can be generalized to test graphs of different sizes and categories.

With 5G deployment gaining momentum, the control-plane traffic volume of cellular networks is escalating. Such rapid traffic growth motivates the need to study the mobile core network (MCN) control-plane design and performance optimization. Doing so requires realistic, large control-plane traffic traces in order to profile and debug the mobile network performance under real workload. However, large-scale control-plane traffic traces are not made available to the public by mobile operators due to business and privacy concerns. As such, it is critically important to develop accurate, scalable, versatile, and open-to-innovation control traffic generators, which in turn critically rely on an accurate traffic model for the control plane. Developing an accurate model of control-plane traffic faces several challenges: (1) how to capture the dependence among the control events generated by each User Equipment (UE), (2) how to model the inter-arrival time and sojourn time of control events of individual UEs, and (3) how to capture the diversity of control-plane traffic across UEs. We present a novel two-level hierarchical state-machine-based control-plane traffic model. We further show how our model can be easily adjusted from LTE to NextG networks (e.g., 5G) to support modeling future control-plane traffic. We experimentally validate that the proposed model can generate large realistic control-plane traffic traces. We have open-sourced our traffic generator to the public to foster MCN research.

The ability to accurately estimate job runtime properties allows a scheduler to effectively schedule jobs. State-of-the-art online cluster job schedulers use history-based learning, which uses past job execution information to estimate the runtime properties of newly arrived jobs. However, with fast-paced development in cluster technology (in both hardware and software) and changing user inputs, job runtime properties can change over time, which lead to inaccurate predictions. In this paper, we explore the potential and limitation of real-time learning of job runtime properties, by proactively sampling and scheduling a small fraction of the tasks of each job. Such a task-sampling-based approach exploits the similarity among runtime properties of the tasks of the same job and is inherently immune to changing job behavior. Our analytical and experimental analysis of 3 production traces with different skew and job distribution shows that learning in space can be substantially more accurate. Our simulation and testbed evaluation on Azure of the two learning approaches anchored in a generic job scheduler using 3 production cluster job traces shows that despite its online overhead, learning in space reduces the average Job Completion Time (JCT) by 1.28×, 1.56×, and 1.32× compared to the prior-art history-based predictor.

Social network de-anonymization, which refers to re-identifying users by mapping an anonymized network to a correlated real-name network, is an important problem in network science that has received intensive study. Although different de-anonymization algorithms have been proposed, the performance limit of any algorithm on a de-anonymization problem remains less explored. In this paper, we investigate the Optimal De-Anonymization Yield (ODAY), i.e., the maximum extent to which the network can be de-anonymized, of a given de-anonymization problem. Specifically, due to the uncertainty of the true mapping, we define ODAY as the maximum expected number of correctly mapped nodes, and propose general approaches for its quantification in general networks. Therefore, ODAY can be viewed as a quantitative and non-asymptotic concretization of the concept of network de-anonymizability, which is mostly investigated in an asymptotic manner in prior art. Inspired by the effect of network symmetry on the de-anonymizability, we show that for a graph pair with arbitrary topologies, ODAY equals the maximum diagonal sum of a matching probability matrix generated from graph homomorphisms. Due to the exponential complexity of enumerating all the possible homomorphisms, we further obtain an upper bound of ODAY by counting the orbits of each of the two graphs, which significantly reduces the computational cost. Two case studies apply our general findings on symmetry and ODAY to specific network models, and a sampling-based algorithm framework is proposed for ODAY calculation in practice. Extensive experiments are performed to validate our findings. To the best of our knowledge, this work is the first effort that quantifies the de-anonymizability of general networks in a non-asymptotic manner from the perspective of network symmetry, and thus sheds light on privacy enhancement for social network design.

Transfer learning does not train from scratch but leverages existing models to help train the new model of better accuracy. Unfortunately, realizing transfer learning in distributed cloud-edge networks faces critical challenges such as online training, uncertain network environments, time-coupled control decisions, and the balance between resource consumption and model accuracy. We formulate distributed transfer learning as a non-linear mixed-integer program of long-term cost optimization. We design polynomial-time online algorithms by exploiting the real-time trade-off between preserving previous decisions and applying new decisions, based on primal-dual one-shot solutions for each single time slot. While orchestrating model placement, data dispatching, and inference aggregation, our approach produces new models via combining the existing offline models and the online models being trained using weights adaptively updated based on inference upon data samples that dynamically arrive. Our approach provably incurs the number of inference mistakes no greater than a constant times that of the single best model in hindsight, and achieves a constant competitive ratio for the total cost. Evaluations have confirmed the superior performance of our approach compared to alternatives on real-world traces.

Motivated by edge computing with artificial intelligence, in this paper we study a bandit-learning problem with switching costs. Existing results in the literature either incur [EQUATION] regret with bandit feedback, or rely on free full-feedback in order to reduce the regret to [EQUATION]. In contrast, we expand our study to incorporate two new factors. First, full feedback could incur a cost. Second, the player may choose 2 (or more) arms at a time, in which case she is free to use any one of the chosen arms to calculate loss, and switching costs are incurred only when she changes the set of chosen arms. For the setting where the player pulls only one arm at a time, our new regret lower-bound shows that, even when costly full-feedback is added, the [EQUATION] regret still cannot be improved. However, the dependence on the number of arms may be improved when the full-feedback cost is small. In contrast, for the setting where the player can choose 2 (or more) arms at a time, we provide a novel online learning algorithm that achieves a lower [EQUATION] regret. Further, our new algorithm does not need any full feedback at all. This sharp difference therefore reveals the surprising power of choosing 2 (or more) arms for this type of bandit-learning problems with switching costs. Both our new algorithm and regret analysis involve several new ideas, which may be of independent interest.

In this paper, we study the generalization performance of overparameterized 3-layer NTK models. We show that, for a specific set of ground-truth functions (which we refer to as the "learnable set"), the test error of the overfitted 3-layer NTK is upper bounded by an expression that decreases with the number of neurons of the two hidden layers. Different from 2-layer NTK where there exists only one hidden-layer, the 3-layer NTK involves interactions between two hidden-layers. Our upper bound reveals that, between the two hidden-layers, the test error descends faster with respect to the number of neurons in the second hidden-layer (the one closer to the output) than with respect to that in the first hidden-layer (the one closer to the input). We also show that the learnable set of 3-layer NTK without bias is no smaller than that of 2-layer NTK models with various choices of bias in the neurons. However, in terms of the actual generalization performance, our results suggest that 3-layer NTK is much less sensitive to the choices of bias than 2-layer NTK, especially when the input dimension is large.

Coflow scheduling improves data-intensive application performance by improving their networking performance. State-of-the-art online coflow schedulers in essence approximate the classic Shortest-Job-First (SJF) scheduling by learning the coflowsizeonline. In particular, they use multiple priority queues to simultaneously accomplish two goals: to sieve long coflows from short coflows, and to schedule short coflows with high priorities. Such a mechanism pays high overhead in learning the coflow size: moving a large coflow across the queues delays small and other large coflows, and moving similar-sized coflows across the queues results in inadvertent round-robin scheduling. We propose Philae, a new online coflow scheduler that exploits the spatial dimension of coflows,i.e.,a coflow has many flows, to drastically reduce the overhead of coflow sizelearning. Philae pre-schedules sampled flows of each coflow and uses their sizes to estimate the average flow size of the coflow. It then resorts to Shortest Coflow First, where the notion of shortest is determined using the learned coflow sizes and coflow contention. We show that the sampling-based learning is robust to flow size skew and has the added benefit of much improved scalability from reduced coordinator-local agent interactions. Our evaluation using an Azure testbed, a publicly available production cluster trace from Facebook shows that compared to the prior art Aalo, Philae reduces the coflow completion time (CCT) in average (P90) cases by$1.50\times $($8.00\times $) on a 150-node testbed and$2.72\times $($9.78\times $) on a 900-node testbed. Evaluation using additional traces further demonstrates Philae’s robustness to flow size skew.

Feature-based student-teacher learning, a training method that encourages the student’s hidden features to mimic those of the teacher network, is empirically successful in transferring the knowledge from a pre-trained teacher network to the student network. Furthermore, recent empirical results demonstrate that, the teacher’s features can boost the student network’s generalization even when the student’s input sample is corrupted by noise. However, there is a lack of theoretical insights into why and when this method of transferring knowledge can be successful between such heterogeneous tasks. We analyze this method theoretically using deep linear networks, and experimentally using nonlinear networks. We identify three vital factors to the success of the method: (1) whether the student is trained to zero training loss; (2) how knowledgeable the teacher is on the clean-input problem; (3) how the teacher decomposes its knowledge in its hidden features. Lack of proper control in any of the three factors leads to failure of the student-teacher learning method.

In this paper, we study the generalization performance of min $\ell_2$-norm overfitting solutions for the neural tangent kernel (NTK) model of a two-layer neural network with ReLU activation that has no bias term. We show that, depending on the ground-truth function, the test error of overfitted NTK models exhibits characteristics that are different from the "double-descent" of other overparameterized linear models with simple Fourier or Gaussian features. Specifically, for a class of learnable functions, we provide a new upper bound of the generalization error that approaches a small limiting value, even when the number of neurons $p$ approaches infinity. This limiting value further decreases with the number of training samples $n$. For functions outside of this class, we provide a lower bound on the generalization error that does not diminish to zero even when $n$ and $p$ are both large.

There has been significant interest in leveraging limited look-ahead to achieve low competitive ratios for online convex optimization (OCO). However, existing online algorithms (such as Averaging Fixed Horizon Control (AFHC)) that can leverage look-ahead to reduce the competitive ratios still produce competitive ratios that grow unbounded as the coefficient ratio (i.e., the maximum ratio of the switching-cost coefficient and the service-cost coefficient) increases. On the other hand, the regularization method can attain a competitive ratio that remains bounded when the coefficient ratio is large, but it does not benefit from look-ahead. In this paper, we propose a new algorithm, called Regularization with Look-Ahead (RLA), that can get the best of both AFHC and the regularization method, i.e., its competitive ratio decreases with the look-ahead window size when the coefficient ratio is small, and remains bounded when the coefficient ratio is large. We also provide a matching lower bound for the competitive ratios of all online algorithms with look-ahead, which differs from the achievable competitive ratio of RLA by a factor that only depends on the problem size. The competitive analysis of RLA involves a non-trivial generalization of online primal-dual analysis to the case with look-ahead.

We study how to schedule data sources in a wireless time-sensitive information system with multiple heterogeneous and unreliable channels to minimize the total expected Age-of-Information (AoI). Although one could formulate this problem as a discrete-time Markov Decision Process (MDP), such an approach suffers from the curse of dimensionality and lack of insights. For single-channel systems, prior studies have developed lower-complexity solutions based on the Whittle index. However, Whittle index has not been studied for systems with multiple heterogeneous channels, mainly because indexability is not well defined when there are multiple dual cost values, one for each channel. To overcome this difficulty, we introduce new notions of partial indexability and partial index, which are defined with respect to one channel's cost, given all other channels' costs. We then combine the ideas of partial indices and max-weight matching to develop a Sum Weighted Index Matching (SWIM) policy, which iteratively updates the dual costs and partial indices. The proposed policy is shown to be asymptotically optimal in minimizing the total expected AoI, under a technical condition on a global attractor property. Extensive performance simulations demonstrate that the proposed policy offers significant gains over conventional approaches by achieving a near-optimal AoI. Further, the notion of partial index is of independent interest and could be useful for other problems with multiple heterogeneous resources.

Graph matching aims to find the latent vertex correspondence between two edge-correlated graphs and has found numerous applications across different fields. In this paper, we study a seeded graph matching problem, which assumes that a set of seeds, i.e., pre-mapped vertex-pairs, is given in advance. While most previous work requires all seeds to be correct, we focus on the setting where the seeds are partially correct. Specifically, consider two correlated graphs whose edges are sampled independently from a parent Erdos-Renyi graph $\mathcal{G}(n,p)$. A mapping between the vertices of the two graphs is provided as seeds, of which an unknown $\beta$ fraction is correct. We first analyze a simple algorithm that matches vertices based on the number of common seeds in the $1$-hop neighborhoods, and then further propose a new algorithm that uses seeds in the $2$-hop neighborhoods. We establish non-asymptotic performance guarantees of perfect matching for both $1$-hop and $2$-hop algorithms, showing that our new $2$-hop algorithm requires substantially fewer correct seeds than the $1$-hop algorithm when graphs are sparse. Moreover, by combining our new performance guarantees for the $1$-hop and $2$-hop algorithms, we attain the best-known results (in terms of the required fraction of correct seeds) across the entire range of graph sparsity and significantly improve the previous results when $p\ge n^{-5/6}$. For instance, when $p$ is a constant or $p=n^{-3/4}$, we show that only $\Omega(\sqrt{n\log n})$ correct seeds suffice for perfect matching, while the previously best-known results demand $\Omega(n)$ and $\Omega(n^{3/4}\log n)$ correct seeds, respectively. Numerical experiments corroborate our theoretical findings, demonstrating the superiority of our $2$-hop algorithm on a variety of synthetic and real graphs.

We investigate competitive online algorithms for online convex optimization (OCO) problems with linear in-stage costs, switching costs and ramp constraints. While OCO problems have been extensively studied in the literature, there are limited results on the corresponding online solutions that can attain small competitive ratios. We first develop a powerful computational framework that can compute an optimized competitive ratio based on the class of affine policies. Our computational framework can handle a fairly general class of costs and constraints. Compared with other competitive results in the literature, a key feature of our proposed approach is that it can handle scenarios where infeasibility may arise due to hard feasibility constraints. Second, we design a robustification procedure to produce an online algorithm that can attain good performance for both average-case and worst-case inputs. We conduct a case study on Network Functions Virtualization (NFV) orchestration and scaling to demonstrate the effectiveness of our proposed methods.

We study low-overhead uplink multi-access algorithms for massive Internet-of-Things (IoT) that can exploit the MIMO performance gain. Although MIMO improves system capacity, it usually requires high overhead due to Channel State Information (CSI) feedback, which is unsuitable for IoT. Recently, a Pseudo-Random Beam-Forming (PRBF) scheme was proposed to exploit the MIMO performance gain for uplink IoT access with uniform channel and load, without collecting CSI at the BS. For non-uniform channel and load, new adaptive beamselection and random-access algorithms are needed to efficiently utilize the system capacity with low overhead. Most existing algorithms for a related multi-channel scheduling problem require each node to at least know some information of the queue length of all contending nodes. In contrast, we propose a new Low-overhead Multi-Channel Joint Channel-Assignment and Random-Access (L-MC-JCARA) algorithm that reduces the overhead to be independent of the number of interfering nodes. A key novelty is to let the BS estimate the total backlog in each contention group by only observing the random-access events, so that no queue-length feedback is needed from IoT devices. We prove that L-MC-JCARA can achieve at least `0.24`` of the capacity region of the optimal centralized scheduler for the corresponding multi-channel system.

Social network de-anonymization, which refers to re-identifying users by mapping their anonymized network to a correlated network, is an important problem that has received intensive study in network science. However, it remains less understood how network structural features intrinsically affect whether or not the network can be successfully de-anonymized. To find the answer, this paper offers the first general study on the relation between de-anonymizability and network symmetry. To this end, we propose to capture the symmetry of a graph by the concept of graph bijective homomorphism. By defining the matching probability matrix, we are able to characterize the de-anonymizability, i.e., the expected number of correctly matched nodes. Specifically, we show that for a graph pair with arbitrary topology, the de-anonymizability is equal to the maximal diagonal sum of the matching probability matrix generated from homomorphisms. Due to the prohibitive cost of enumerating all possible homomorphisms, we further obtain an upper bound of such de-anonymizability by counting the orbits of each of the two graphs, which significantly reduces the computational cost. Such a general result allows us to theoretically obtain the de-anonymizability of any networks with more specific topology structure. For example, for any classic Erdős-Rènyi graph with designated n and p, we can represent its de-anonymizability numerically by calculating the local symmetric structure that it contains. Extensive experiments are performed to validated our findings.

Recently, there have been significant interests in studying the so-called "double-descent" of the generalization error of linear regression models under the overparameterized and overfitting regime, with the hope that such analysis may provide the first step towards understanding why overparameterized deep neural networks (DNN) still generalize well. However, to date most of these studies focused on the min L2-norm solution that overfits the data. In contrast, in this paper we study the overfitting solution that minimizes the L1-norm, which is known as Basis Pursuit (BP) in the compressed sensing literature. Under a sparse true linear regression model with p i.i.d. Gaussian features, we show that for a large range of p up to a limit that grows exponentially with the number of samples n, with high probability the model error of BP is upper bounded by a value that decreases with p. To the best of our knowledge, this is the first analytical result in the literature establishing the double-descent of overfitting BP for finite n and p. Further, our results reveal significant differences between the double-descent of BP and min L2-norm solutions. Specifically, the double-descent upper-bound of BP is independent of the signal strength, and for high SNR and sparse models the descent-floor of BP can be much lower and wider than that of min L2-norm solutions.

Renewable energy generations and energy storage are playing increasingly important roles in serving consumers in power systems. This paper studies the market competition between renewable energy suppliers with or without energy storage in a local energy market. The storage investment brings the benefits of stabilizing renewable energy suppliers' outputs, but it also leads to substantial investment costs as well as some surprising changes in the market outcome. To study the equilibrium decisions of storage investment in the renewable energy suppliers' competition, we model the interactions between suppliers and consumers using a three-stage game-theoretic model. In Stage I, at the beginning of the investment horizon (containing many days), suppliers decide whether to invest in storage. Once such decisions have been made (once), in the day-ahead market of each day, suppliers decide on their bidding prices and quantities in Stage II, based on which consumers decide the electricity quantity purchased from each supplier in Stage III. In the real-time market, a supplier is penalized if his actual generation falls short of his commitment. We characterize a price-quantity competition equilibrium of Stage II in the local energy market, and we further characterize a storage-investment equilibrium in Stage I incorporating electricity-selling revenue and storage cost. Counter-intuitively, we show that the uncertainty of renewable energy without storage investment can lead to higher supplier profits compared with the stable generations with storage investment due to the reduced market competition under random energy generation. Simulations further illustrate results due to the market competition. For example, a higher penalty for not meeting the commitment, a higher storage cost, or a lower consumer demand can sometimes increase a supplier's profit. We also show that although storage investment can increase a supplier 's profit, the first-mover supplier who invests in storage may benefit less than the free-rider competitor who chooses not to invest in storage.

A pseudo-random beamforming (PRBF) based random access (RA) system is proposed to enable uplink (UL) machine-type communications (MTC) with ultra low signaling overheads. Specifically, a pseudo random (PR) sequence is used as public information to coordinate the beamforming vectors used at the base station (BS) and the devices. Within the coherence time window, each device distributively determines in advance the ''good'' time slots and receiving beams for transmission. This UL protocol reduces the overheads due to the feedback of channel state information and the control signals for centralized scheduling. This paper derives the throughput and user scaling of the proposed M- PRBF-CA protocol for achieving spatial multiplexing gain, under both an i.i.d. slow fading channel and a correlated slow fading channel. Our simulation results confirm the analysis in both fading channel models.

Renewable energy resources are playing an increasingly important role in serving consumers at the distribution level of power systems. This paper studies a duopoly two-settlement local renewable energy market, in which one energy supplier has controllable generations (with the help of energy storage) while the other supplier has random generations. In the day-ahead energy market, suppliers determine the bidding prices and quantities, and then consumers decide the energy quantity to purchase from each supplier. In the real-time energy market, a supplier gets penalized if he cannot deliver the amount of energy as committed in the day-ahead market. We formulate the interactions between suppliers and consumers in the day-ahead market as a two-stage problem. The two-dimensional bidding strategies (price and quantity) in the day-ahead market together with the penalty in the real-time market increase the complexity of the equilibrium analysis. To address such a challenge, we first derive weakly dominant bidding quantity strategies for both suppliers, and then characterize the corresponding pure and mixed price equilibrium. We demonstrate that the supplier with controllable generations can earn a much higher payoff than the supplier with random generations. In some cases, however, we show the perhaps counterintuitive result that a higher penalty or a higher variance of random generations may increase both suppliers' payoffs.

Coded caching can exploit multicast opportunities even when multiple users request different pieces of content, and thus can significantly reduce the backhaul requirement to serve high-volume content. A common assumption in existing studies of coded caching is that all files are with the same size, which however may not be true in reality. Our previous work [1] first studied this problem, and proposed a non-trivial lower bound, as well as a new achievable scheme that uses a caching probability increasing proportionally with the file size. However, the gap [1] of the achievable rate and the lower bound still differs by a factor of Θ(log K), where K is the number of users in the system. In this paper, under a mild assumption that the total size of all files is larger than eight times the size of one individual cache, we will close this gap and reduce it to a constant by proposing a novel new lower bound and another new achievable scheme. Our lower bound is derived by considering a new cut-set bound, where files of a type1will be requested more often if the number of such files is smaller. Our achievable scheme uses a caching probability that decreases with the number of files with a same type. The improvements on both the lower bound and the achievable rate make their gap constant.

Operating distributed Scrubbing Centers (SCs) to mitigate massive Distributed Denial of Service (DDoS) traffic in large-scale networks faces critical challenges. The operator needs to determine the diversion rule installation and elimination in the networks, as well as the scrubbing resource activation and revocation in the SCs, while minimizing the long-term cost and the cumulative decision-switching penalty without knowing the exact amount of the malicious traffic. We model and formulate this problem as an online nonlinear integer program. In contrast to many other online problems where future inputs are unknown but at least current inputs are known, a key new challenge here is that even part of the current inputs are unknown when decisions are made. To "learn" the best decisions online, we transform our problem via a gap-preserving approximation into an online optimization problem with only the known inputs, which is further relaxed and decoupled into a series of one-shot convex programs solvable in individual time slots. To overcome the intractability, we design a progressive rounding algorithm to convert fractional decisions into integral ones without violating the constraints. We characterize the competitive ratio of our approach as a function of the key parameters of our problem. We conduct evaluations using real-world data and confirm our algorithms' superiority over de facto practices and state-of-the-art methods.

Ride-sharing is a modern urban-mobility paradigm with tremendous potential in reducing congestion and pollution. Demand-aware design is a promising avenue for addressing a critical challenge in ridesharing systems, namely joint optimization of request-vehicle assignment and routing for a fleet of vehicles. In this paper, we develop a probabilistic demand-aware framework to tackle the challenge. We focus on maximizing the expected number of passenger pickups, given the probability distributions of future demands. The key idea of our approach is to assign requests to vehicles in a probabilistic manner. It differentiates our work from existing ones and allows us to explore a richer design space to tackle the request-vehicle assignment puzzle with a performance guarantee but still keeping the final solution practically implementable. The optimization problem is non-convex, combinatorial, and NP-hard in nature. As a key contribution, we explore the problem structure and propose an elegant approximation of the objective function to develop a dual-subgradient heuristic. We characterize a condition under which the heuristic generates a (1 -- 1/e) approximation solution. Our solution is simple and scalable, amendable for practical implementation. Results of numerical experiments based on real-world traces in Manhattan show that, as compared to a conventional demand-oblivious scheme, our demand-aware solution improves the passenger pickups by up to 46%. The results also show that joint optimization at the fleet level leads to 19% more pickups than that by separate optimizations at individual vehicles.

We study the source detection problem using limited timestamps on a given network. Due to the NP-completeness of the maximum likelihood estimator (MLE), we propose an approximation solution called infection-path-based estimator (INF), the essence of which is to identify the most likely infection path that is consistent with observed timestamps. The source node associated with that infection path is viewed as the estimated source û. For the tree network, we transform the INF into integer linear programming and find a reduced search region using BFS, within which the estimated source is provably always on a path termed as candidate path. This notion enables us to analyze the accuracy of the INF in terms of error distance on arbitrary tree. Specifically, on the infinite g-regular tree with uniform sampled timestamps, we get a refined performance guarantee in the sense of a constant bounded d(u*, û). By virtue of time labeled BFS tree, the estimator still performs fairly well when extended to more general graphs. Simulations on both trees and general networks further demonstrate the superior performance of the INF.

To realize mobile virtual reality (VR) group gaming services which are currently hampered by the prohibitive bandwidth and the stringent delay requirements, we investigate the problem of provisioning such services using the emerging mobile edge cloudlet (MEC) networks with a distributed content rendering architecture. The underlying dynamic rendering-module placement problem requires to optimize the service’s operational cost and the users’ end-to-end performance, involving multiple intertwined conflicting system objectives that are discrete, nonconvex, and higher degree polynomial functions with coupled decisions and arbitrary user dynamics over time. We solve this online placement problem by leveraging model predictive control (MPC) and overcoming the aforementioned challenges over each prediction window. We explore the connection between the placement problem and the minimal$s$-$t$cut problem in graph theory and solve the former via solving a series of instances of the latter. We formally prove the performance guarantee of our approach. We also conduct extensive trace-driven evaluations and demonstrate the superior practical performance of our MPC-based approach compared to thede factopractices and the state-of-the-art alternatives.

We investigate competitive online algorithms for online convex optimization (OCO) problems with linear in-stage costs, switching costs and ramp constraints. While OCO problems have been extensively studied in the literature, there are limited results on the corresponding online solutions that can attain small competitive ratios. We first develop a powerful computational framework that can compute an optimized competitive ratio based on the class of affine policies. Our computational framework can handle a fairly general class of costs and constraints. Compared to other competitive results in the literature, a key feature of our proposed approach is that it can handle scenarios where infeasibility may arise due to hard feasibility constraints. Second, we design a robustification procedure to produce an online algorithm that can attain good performance for both average-case and worst-case inputs. We conduct a case study on Network Functions Virtualization (NFV) orchestration and scaling to demonstrate the effectiveness of our proposed methods.

The uncertainty and variability of renewable generation pose significant challenges to reliable power-grid operations. This paper designs robust online strategies for jointly operating energy storage units and fossil-fuel generators to achieve provably reliable grid operations at all times under high renewable uncertainty, without the need of renewable curtailment. In particular, we jointly consider two power system operations, namely day-ahead reliability assessment commitment (RAC) and real-time dispatch. We first extend the concept of “safe-dispatch sets” to our setting. While finding such safe-dispatch sets and checking their non-emptiness provide crucial answers to both RAC and real-time dispatch, their computation incurs high complexity in general. To develop computationally-efficient solutions, we first study a single-bus case with one generator-storage pair, where we derive necessary conditions and sufficient conditions for the safe-dispatch sets. Our results reveal fundamental trade-offs between storage capacity and generator ramp-up/-down limits to ensure grid reliability. Then, for the more general multi-bus scenario, we split the net-demand among virtual generator-storage pairs (VGSPs) and apply our single-bus decision strategy to each VGSP. Simulation results on an IEEE 30-bus system show that, compared with state-of-art solutions, our scheme requires significantly less storage to ensure reliable grid operation without any renewable curtailment.

Operating distributed cloudlets at optimal cost is nontrivial when facing not only the dynamic and unpredictable resource prices and user requests, but also the low efficiency of today's immature cloudlet infrastructures. We propose to control cloudlet networks at multiple granularities: fine-grained control of servers inside cloudlets and coarse-grained control of cloudlets themselves. We model this problem as a mixed-integer nonlinear program with the switching cost over time. To solve this problem online, we firstly linearize, "regularize", and decouple it into a series of one-shot subproblems that we solve at each corresponding time slot, and afterwards we design an iterative, dependent rounding framework using our proposed randomized pairwise rounding algorithm to convert the fractional control decisions into the integral ones at each time slot. Via rigorous theoretical analysis, we exhibit our approach's performance guarantee in terms of the competitive ratio and the multiplicative integrality gap towards the offline optimal integral decisions. Extensive evaluations with real-world data confirm the empirical superiority of our approach over the single granularity server control and the state-of-the-art algorithms.

Caching plays an important role in reducing the backbone traffic when serving high-volume multimedia content. Recently, a new class of coded caching schemes have received significant interest, because they can exploit coded multi-cast opportunities to further reduce backbone traffic. Without considering file popularity, prior works have characterized the fundamental performance limits of coded caching through a deterministic worst-case analysis. However, when heterogeneous file popularity is considered, there remain open questions regarding the fundamental limits of coded caching performance. In this paper, for an arbitrary popularity distribution, we first derive a new information-theoretic lower bound on the expected transmission rate of any coded caching schemes. We then show that a simple coded-caching scheme attains an expected transmission rate that is at most a constant factor away from the lower bound. Unlike other existing studies, the constant factor that we derived is independent of the popularity distribution.

An emerging solution to privacy issues in smart grids is battery-based load hiding (BLH) that uses a rechargeable battery to decouple the meter readings from user activities. However, existing BLH algorithms have two significant limitations: (1) Most of them focus on flattening high-frequency variation of usage profile only, thereby still revealing a low-frequency shape, (2) Otherwise, they assume to know a statistical model of usage pattern. To overcome these limitations, we propose a new BLH algorithm, named RL-BLH. The RL-BLH hides both low-frequency and high-frequency usage patterns by shaping the meter readings to rectangular pulses. The RL-BLH learns a decision policy for choosing pulse magnitudes on the fly without prior knowledge of usage pattern. The decision policy is designed to charge and discharge the battery in the optimal way to maximize cost savings. We also provide heuristics to shorten learning time and improve cost savings.

This paper studies a nanosensor coordination scheme to effectively deliver nanosensors to deep targets. Deep targets are far away from the main patrolling paths of nanosensors (e.g. blood vessels) and hence the delivery ratio relying on natural diffusion can be very low. Inspired by the communication and motility capability of bacteria, we devise a decentralized coordination strategy so that once the deep target is identified by a small number of nanosensors, they can effectively recruit far-away nanosensors towards the target. Note that since the target is deep, patrolling nanosensors are typically outside the direct communication range of those nanosensors at the location of the target. Therefore, multi-hop communication is required to recruit replenishing agents from the main paths. We demonstrate that the proposed strategy can successfully pull the patrolling nanosensors to the deep target when the model parameters are properly selected. This suggests a potential solution to the open problem in cancer treatments that therapeutic agents are kept away from the central necrotic core of tumors.

This paper develops a novel business model to enable virtual storage sharing among a group of users. Specifically, an aggregator owns a central physical storage unit and virtualizes the physical storage into separable virtual storage capacities that can be sold to users. Each user purchases the virtual storage capacity, and schedules the charge and discharge of the virtual storage to reduce his peak power consumption. We formulate the interaction between the aggregator and users in each operation horizon as a two-stage problem. At the beginning of the operation horizon, the aggregator first determines the unit price of virtual storage capacity to maximize her profit in Stage 1, and users decide the capacities to purchase and the storage scheduling during the operation horizon in Stage 2. Since the closed-form solution is not available and the decisions are coupled across the two stages, we characterize the solutions of the two-stage problem based on parametric linear programming. Simulation results show that compared to the case where each user acquires his own physical storage, storage virtualization reduces the overall physical capacity needed for all users by 34.9%, and the overall physical power rating by 45.1%.

A common feature among many crowdsourcing applications is to decompose the huge or complex tasks into some small sub-ones, which require some users with different skills to implement. The kind of tasks are composite and called Composite Tasks (CTs) , which are said to be completed and return reward only after all of their sub-tasks are finished successfully. Meanwhile, users may have various capabilities to implement diverse sub-tasks (STs) with corresponding cost so users are heterogeneous. In this paper, we study the problem of how users choose the STs to maximize their payoff (reward minus cost) when there are multiple such CTs. This payoff maximization problem with multiple CTs and heterogeneous users turns out to be NP-completed. We then propose a Local Composite Task Selection (LCTS) algorithm to help the users choose their subtask strategies. Its convergence and complexity are analyzed theoretically. For comparison, we design a centralized Composite Task Selection (CTS) algorithm and a Low Cost and Random sub-task selection (LCR) algorithm as benchmarks. Numerical results suggest that the LCTS algorithm achieves a similar payoff and task completion ratio to the CTS when the number of users is large. The performance of LCTS is highly over LCR on both of the payoff and the task completion ratio. The results also illustrate the quick convergence of the LCTS algorithm.

Next generation wireless networks will carry traffic from a wide range of applications, and many of them may require packets to be delivered before their respective deadlines. In this paper, we investigate using inter-session network coding to send packets wirelessly for two deadline-constrained unicast sessions. In particular, each unicast session aims to transmit a file, whose packets have hard sequential deadline constraints. We first characterize the corresponding deadline-constrained capacity region under heterogeneous channel conditions and heterogeneous deadline constraints. We show that this deadline-constrained capacity region can be achieved asymptotically by modifying the existing generation-based (G-B) schemes. However, despite its asymptotic optimality, the G-B scheme has very poor performance for small and medium file sizes. To address these problems, we develop a new immediately-decodable network coding (IDNC) scheme that empirically demonstrates much better performance for short file sizes, and we prove analytically its asymptotic optimality when used to send large files. Our analysis uses a novel version of drift analysis, which could also be of independent interest to other IDNC schemes.

In this paper, we are interested in online multistage decisions to ensure robust power grid operations under high renewable uncertainty. We jointly consider both the reliability assessment commitment (RAC) and the real-time dispatch problems. We first focus on the real-time dispatch problem and define “maximally robust algorithms,” which can provably ensure grid safety whenever there exists any other algorithm that can ensure grid safety under the same level of future uncertainty. We characterize a class of maximally robust algorithms using the concept of “safe dispatch set,” which also provides conditions for verifying grid safety for RAC. However, in general such safe dispatch sets may be difficult to compute. We then develop efficient computational algorithms for characterizing the safe dispatch sets. Specifically, for a simpler single-bus two-generator case, we show that the safe dispatch sets can be exactly characterized by a polynomial number of convex constraints. Then, based on this two-generator characterization, we develop a new solution for the multi-bus multi-generator case using the idea of virtual demand splitting (VDS), which can effectively compute a suitable subset of the safe-dispatch set. Our numerical results demonstrate that a VDS-based economic dispatch algorithm outperforms the standard economic dispatch algorithm in terms of robustness, without sacrificing economy.

In this paper, we study how to cluster Remote Radio Heads (RRHs) into Virtual Base-Stations (VBSs) in a Cloud-based Radio Access Network to optimally manage the tradeoff between improving the performance of cell-edge users and maintaining high spatial reuse for the overall system. We develop Gibbs-sampling based algorithms that can find the desirable global VBS configuration from an arbitrarily given set of allowable VBS configurations. While Gibbs-sampling has been used to solve other wireless control problems, its application to VBS clustering faces new challenges both due to the difficulty in estimating the quality of a VBS configuration under rapid channel variations, and due to a new global coupling effect. We leverage Random Matrix Theory to develop a method that can quickly estimate the quality of a VBS configuration based only on average channel statistics. Further, we use perturbation analysis to develop a distributed approximation of the Gibbs sampler to circumvent the global coupling effect, which then allows different parts of the network to search for better VBS configurations in parallel. Our numerical results demonstrate how the proposed algorithm can be used as a general tool to evaluate the system performance under a variety of clustering constraints.

It has been known that scheduling algorithms designed to achieve throughput optimality and good delay performance often require solving the Maximum Weighted Independent Set (MWIS) problem. However, under most realistic network settings, the MWIS problem is known to be NP-hard. In non-fading environments, low-complexity scheduling algorithms have been provided that converge either to the MWIS solution in time or to a solution that achieves at least a provable fraction of the achievable throughput. However, in more practical systems the channel conditions can vary at faster time-scales than convergence occurs in these lower-complexity algorithms. Hence, these algorithms cannot take advantage of opportunistic gains, and may no longer result in achieving good performance. In this paper, we propose a low-complexity scheduling scheme that performs provably well under fading channels and is amenable to implement in a distributed manner. To the best of our knowledge, this is the first scheduling scheme under fading environments that requires only local information, has a low complexity that grows logarithmically with the network size (provided that the conflict graph has bounded maximum vertex degree), and achieves provable performance guarantees (arbitrarily close to that of the well-known centralized Greedy Maximal Scheduler). We verify that the throughput and the delay of our proposed scheme are close to those of the optimal MaxWeight that solves MWIS at each time. Further, we implement our algorithm in a testbed by modifying the existing IEEE 802.11 DCF. The experiment results show that our implementation successfully accounts for wireless fading, attains the short-term opportunistic gains in practice, and hence substantially outperforms IEEE 802.11 DCF.

Although cellular networks can be provisioned according to the peak demand, they usually experience large fluctuations in both channel conditions and traffic load level. Scheduling with both channel and load awareness allows us to exploit the delay tolerance of data traffic to alleviate network congestion, and thus reduce the peak. However, solving the optimal scheduling problem leads to a large-scale Markov decision process (MDP) with extremely high complexity. In this paper, we propose a scalable and distributed approach to this problem, called Coordinated Scheduling (CoSchd). CoSchd decomposes the large-scale MDP problem into many individual MDP problems, each of which can be solved independently by each user under a limited amount of coordination signals from the base station (BS). We show that CoSchd is close to optimal when the number of users becomes large. Furthermore, we propose an approximation of CoSchd that iteratively updates the scheduling policy based on online measurements. Simulation results demonstrate that exploiting channel and load awareness with CoSchd can effectively alleviate cellular network congestion.

Opportunistic scheduling of delay-tolerant traffic has been shown to substantially improve spectrum efficiency. To encourage users to adopt delay-tolerant scheduling for capacity -improvement, it is critical to provide guarantees in terms of completion time. In this paper, we study application-level scheduling with deadline constraints, where the deadline is pre-specified by users/applications and is associated with a deadline violation probability. To address the exponentially-high complexity due to temporally-varying channel conditions and deadline constraints, we develop a novel asymptotic approach that exploits the largeness of the network to our advantage. Specifically, we identify a lower bound on the deadline violation probability, and propose simple policies that achieve the lower bound in the large-system regime. The results in this paper thus provide a rigorous analytical framework to develop and analyze policies for application-level scheduling under very general settings of channel models and deadline requirements. Further, based on the asymptotic approach , we propose the notion of Application-Level Effective Capacity region, i.e., the throughput region that can be supported subject to deadline constraints, which allows us to quantify the potential gain of application-level scheduling. Simulation results show that application-level scheduling can improve the system capacity significantly while guaranteeing the deadline constraints.

In this paper, we study the problem of link scheduling for multi-hop wireless networks with per-flow delay constraints under the$K$-hop interference model. Specifically, we are interested in algorithms that maximize the asymptotic decay-rate of the probability with which the maximum end-to-end backlog among all flows exceeds a threshold, as the threshold becomes large. We provide both positive and negative results in this direction. By minimizing the drift of the maximum end-to-end backlog in the converge-cast on a tree, we design an algorithm, Largest-Weight-First (LWF), that achieves the optimal asymptotic decay-rate for the overflow probability of the maximum end-to-end backlog as the threshold becomes large. However, such a drift minimization algorithm may not exist for general networks. We provide an example in which no algorithm can minimize the drift of the maximum end-to-end backlog. Finally, we simulate the LWF algorithm together with a well known algorithm (the back-pressure algorithm) and a large-deviations optimal algorithm in terms of the sum-queue (the P-TREE algorithm) in converge-cast networks. Our simulation shows that our algorithm performs significantly better not only in terms of asymptotic decay-rate, but also in terms of the actual overflow probability.

Peer-to-peer (P2P) streaming technologies can take advantage of the upload capacity of clients, and hence can scale to large content distribution networks with lower cost. A fundamental question for P2P streaming systems is the maximum streaming rate that all users can sustain. Prior works have studied the optimal streaming rate for a complete network, where every peer is assumed to be able to communicate with all other peers. This is, however, an impractical assumption in real systems. In this paper, we are interested in the achievable streaming rate when each peer can only connect to a small number of neighbors. We show that even with a random peer-selection algorithm and uniform rate allocation, as long as each peer maintains Ω(logN) downstream neighbors, where N is the total number of peers in the system, the system can asymptotically achieve a streaming rate that is close to the optimal streaming rate of a complete network. These results reveal a number of important insights into the dynamics of the system, based on which we then design simple improved algorithms that can reduce the constant factor in front of the Ω(logN) term, yet can achieve the same level of performance guarantee. Simulation results are provided to verify our analysis.

The performance of large-scale peer-to-peer (P2P) video-on-demand (VoD) streaming systems can be very challenging to analyze due to sparse connectivity and complex, random dynamics. Specifically, in practical P2P VoD systems, each peer only interacts with a small number of other peers/neighbors. Furthermore, its upload capacity, downloading position, and content availability change dynamically and randomly. In this paper, we rigorously study large-scale P2P VoD systems with sparse connectivity among peers and investigate simple and decentralized P2P control strategies that can provably achieve close-to-optimal streaming capacity. We first focus on a single streaming channel. Using a simple algorithm that assigns each peer a random set of Θ(logN) neighbors and allocates upload capacity uniformly, we show that a close-to-optimal streaming rate can be asymptotically achieved for all peers with high probability as the number of peers N increases. Furthermore, the tracker does not need to obtain detailed knowledge of which chunks each peer caches, and hence incurs low overhead. We then study multiple streaming channels where peers watching one channel may help peers in another channel with insufficient upload bandwidth. We propose a simple random cache-placement strategy and show that a close-to-optimal streaming capacity region for all channels can be attained with high probability, again with only Θ(logN) per-peer neighbors. These results provide important insights into the dynamics of large-scale P2P VoD systems, which will be useful for guiding the design of improved P2P control protocols.

We study competitive online algorithms for EV (electrical vehicle) charging under the scenario of an aggregator serving a large number of EVs together with its background load, using both its own renewable energy (for free) and the energy procured from the external grid. The goal of the aggregator is to minimize its peak procurement from the grid, subject to the constraint that each EV has to be fully charged before its deadline. Further, the aggregator can predict the future demand and the renewable energy supply with some levels of uncertainty. The key challenge here is how to develop a model that captures the prior knowledge from such prediction, and how to best utilize this prior knowledge to reduce the peak under future uncertainty. In this paper, we first propose a 2-level increasing precision model (2-IPM), to capture the system uncertainty. We develop a powerful computation approach that can compute the optimal competitive ratio under 2-IPM over any online algorithm, and also online algorithms that can achieve the optimal competitive ratio. A dilemma for online algorithm design is that an online algorithm with good competitive ratio may exhibit poor average-case performance. We then propose a new Algorithm-Robustification procedure that can convert an online algorithm with reasonable average-case performance to one with both the optimal competitive ratio and good average-case performance. The robustified version of a well-known heuristic algorithm, Receding Horizon Control (RHC), is found to demonstrate superior performance via trace-based simulations.

Coded caching can exploit new multicast opportunities even when multiple users request different pieces of content, and thus can significantly reduce the backhaul requirement for serving high-volume content. However, existing studies of coded caching have been limited to the scenarios where all files of interest are of a common size. This work studies the performance limits of coded caching when the file sizes are different. We derive a new lower bound and an achievable upper bound for the worst-case transmission rate under coded caching, and show that these two bounds differ by at most a Θ(log K) factor, where K is the number of users in the system. There are two key novelties in our analysis. First, our lower bound is derived by considering a new cut-set bound where larger files are requested more times. The analysis of this new cut-set bound requires careful concatenation of several entropy inequalities. Compared to a lower bound using standard cut-set arguments, our lower bound is improved by a Θ(log K) factor. Second, our achievable scheme uses a caching probability that increases proportionally with the file size. Compared to schemes that use a common caching probability, the achievable rate of our scheme is reduced by a Θ K/logk2factor.

Carrier-sense multiple access (CSMA) algorithms have recently received significant interests in the literature for designing wireless control algorithms. CSMA algorithms incur low complexity and can achieve the optimal capacity under certain assumptions. However, CSMA algorithms suffer the starvation problem and incur large delay that may grow exponentially with the network size. In this paper, our goal is to develop a new algorithm that can provably achieve high throughput utility and low delay with low complexity. Toward this end, we propose a new CSMA-like algorithm, called Virtual-Multi-Channel CSMA (VMC-CSMA), that can dramatically reduce delay. The key idea of VMC-CSMA to avoid the starvation problem is to use multiple virtual channels (which emulate a multichannel system) and compute a good set of feasible schedules simultaneously (without constantly switching/recomputing schedules). Under the protocol interference model and a single-hop utility-maximization setting, VMC-CSMA can approach arbitrarily close-to-optimal system utility with both the number of virtual channels and the computation complexity increasing logarithmically with the network size. Furthermore, once VMC-CSMA converges to the steady state, we can show that under certain assumptions on the utility functions and the topology, both the expected packet delay and the tail distribution of the head-of-line (HOL) waiting time at each link can be bounded independently of the network size. Our simulation results confirm that VMC-CSMA algorithms indeed achieve both high throughput utility and low delay with low-complexity operations.

In this paper, we focus on the scheduling problem in multichannel wireless networks, e.g., the downlink of a single cell in fourth-generation (4G) OFDM-based cellular networks. Our goal is to design practical scheduling policies that can achieve provably good performance in terms of both throughput and delay, at a low complexity. While a class of O(n2.5log n)-complexity hybrid scheduling policies is recently developed to guarantee both rate-function delay optimality (in the many-channel many-user asymptotic regime) and throughput optimality (in the general non-asymptotic setting), their practical complexity is typically high. To address this issue, we develop a simple greedy policy called Delay-based Server-Side-Greedy (D-SSG) with a lower complexity 2n2+2n, and rigorously prove that D-SSG not only achieves throughput optimality, but also guarantees near-optimal asymptotic delay performance. Specifically, the rate-function of the delay-violation probability attained by D-SSG for any fixed integer delay threshold b > 0 is no smaller than the maximum achievable rate-function by any scheduling policy for threshold b-1. Thus, we are able to achieve a reduction in complexity (from O(n2.5logn) of the hybrid policies to 2n2+ 2n) with a minimal drop in the delay performance. More importantly, in practice, D-SSG generally has a substantially lower complexity than the hybrid policies that typically have a large constant factor hidden in the O(·) notation. Finally, we conduct simulations to validate our theoretical results in various scenarios. The simulation results show that in all scenarios we consider, D-SSG not only guarantees a near-optimal rate-function, but also empirically has a similar delay performance to the rate-function delay-optimal policies.

Online microblogging sites have become increasingly important platforms for information diffusion in today's world, where users post short messages and follow various messages posted by people that they are interested in. It is intriguing to qualitatively study the temporal dynamics of an information cascade in a microblogging system, in terms of the number of users influenced at any given time, which may provide valuable input to facilitate emerging applications such as online advertising and content distribution. In this paper, we model information diffusion in a microblogging network as an age-dependent branching process, based on practical observations from Tencent Weibo, a popular microblogging site in China. This model enables careful characterization of the diffusion topology, the different delays for users to respond to new information, and the evolution of the size of the information cascade over time. We derive the expected cascade size at any time. We validate our model based on Tencent Weibo traces, and demonstrate its effectiveness in capturing information diffusion dynamics in the real world.

Opportunistic scheduling of delay-tolerant traffic has been shown to substantially improve spectrum efficiency. To encourage users to adopt delay-tolerant scheduling for capacity-improvement, it is critical to provide guarantees in terms of completion time. In this paper, we study application-level scheduling with deadline constraints, where the deadline is pre-specified by users/applications and is associated with a deadline violation probability. To address the exponentially-high complexity due to temporally-varying channel conditions and deadline constraints, we develop a novel asymptotic approach that exploits the largeness of the network to our advantage. Specifically, we identify a lower bound on the deadline violation probability, and propose simple policies that achieve the lower bound in the large-system regime. The results in this paper thus provide a rigorous analytical framework to develop and analyze policies for application-level scheduling under very general settings of channel models and deadline requirements. Further, based on the asymptotic approach, we propose the notion of Application-Level Effective Capacity region, i.e., the throughput region that can be supported subject to deadline constraints, which allows us to quantify the potential gain of application-level scheduling.

SVC-based live video-streaming in multi-channel wireless networks leads to a challenging joint rate-control and scheduling problem with stringent deadline constraints. Traditional utility-based approaches often did not explicitly account for deadlines. In this paper, we explicitly account for deadlines and study the problem of optimizing the total reward from packets meeting their deadlines in a modern 4G OFDM system. Motivated by a heuristic utility-based approach, we propose a class of threshold-based rate-control and wireless scheduling policies that can respect the deadline constraints and approach the optimal system reward asymptotically as the system size increases. We also propose a distributed realization of our threshold-based policies that can be easily implemented in practical scenarios. We substantiate the result via both analysis and simulation.

In this paper, we study the scheduling problem for downlink transmission in a multichannel (e.g., OFDM-based) wireless network. We focus on a single cell, with the aim of developing a unifying framework for designing low-complexity scheduling policies that can provide optimal performance in terms of both throughput and delay. We develop new easy-to-verify sufficient conditions for rate-function delay optimality (in the many-channel many-user asymptotic regime) and throughput optimality (in general nonasymptotic setting), respectively. The sufficient conditions allow us to prove rate-function delay optimality for a class of Oldest Packets First (OPF) policies and throughput optimality for a large class of Maximum Weight in the Fluid limit (MWF) policies, respectively. By exploiting the special features of our carefully chosen sufficient conditions and intelligently combining policies from the classes of OPF and MWF policies, we design hybrid policies that are both rate-function delay-optimal and throughput-optimal with a complexity of O(n2.5log n), where n is the number of channels or users. Our sufficient condition is also used to show that a previously proposed policy called Delay Weighted Matching (DWM) is rate-function delay-optimal. However, DWM incurs a high complexity of O(n5). Thus, our approach yields significantly lower complexity than the only previously designed delay and throughput-optimal scheduling policy. We also conduct numerical experiments to validate our theoretical results.

CSMA algorithms have recently received a significant amount of interest in the literature for designing efficient wireless control algorithms. CSMA algorithms are attractive because they incur low computation complexity and communication overhead, and can be shown to achieve the optimal capacity under certain assumptions. However, it has also been observed that CSMA algorithms suffer the starvation problem and incur large delay that may grow exponentially with the network size. In this paper, we propose a new algorithm, called Virtual-Multi-Channel (VMC-) CSMA, that can dramatically reduce delay without sacrificing the high capacity and low complexity of CSMA. The key idea of VMC-CSMA to avoid the starvation problem is to use multiple virtual channels to emulate a multi-channel system and compute a good set of feasible schedules simultaneously (without constantly switching/re-computing schedules). Under the protocol interference model and a single-hop utility-maximization setting, our proposed VMC-CSMA algorithm can approach arbitrarily close to the optimal total system utility, with both the number of virtual channels and the computation complexity increasing logarithmically with the network size. The VMC-CSMA algorithm inherits the distributed nature of CSMA algorithms. Further, once our algorithm converges to the steady-state, the expected packet delay for each link equals to the inverse of its long-term average rate, and the distribution of its head-of-line (HOL) waiting time can also be asymptotically bounded. Our simulation results confirm that the proposed VMC-CSMA algorithm indeed achieves both high throughput and low delay. Further, it can quickly adapt to network traffic changes.

In this paper, we focus on the scheduling problem in multi-channel wireless networks, e.g., the downlink of a single cell in fourth generation (4G) OFDM-based cellular networks. Our goal is to design efficient scheduling policies that can achieve provably good performance in terms of both throughput and delay, at a low complexity. While a recently developed scheduling policy, called Delay Weighted Matching (DWM), has been shown to be both rate-function delay-optimal (in the many-channel many-user asymptotic regime) and throughput-optimal (in general non-asymptotic setting), it has a high complexity O(n5), which makes it impractical for modern OFDM systems. To address this issue, we first develop a simple greedy policy called Delay-based Queue-Side-Greedy (D-QSG) with a lower complexity O(n3), and rigorously prove that D-QSG not only achieves throughput optimality, but also guarantees near-optimal rate-function-based delay performance. Specifically, the rate-function attained by D-QSG for any fixed integer threshold b>0, is no smaller than the maximum achievable rate-function by any scheduling policy for threshold b-1. Further, we develop another simple greedy policy called Delay-based Server-Side-Greedy (D-SSG) with an even lower complexity O(n2), and show that D-SSG achieves the same performance as D-QSG. Thus, we are able to achieve a dramatic reduction in complexity (from O(n5) of DWM to O(n2)) with a minimal drop in the delay performance. Finally, we conduct numerical simulations to validate our theoretical results in various scenarios. The simulation results show that our proposed greedy policies not only guarantee a near-optimal rate-function, but also empirically are virtually indistinguishable from the delay-optimal policy DWM.

The performance of large-scaled peer-to-peer (P2P) video-on-demand (VoD) streaming systems can be very challenging to analyze. In practical P2P VoD systems, each peer only interacts with a small number of other peers/neighbors. Further, its upload capacity may vary randomly, and both its downloading position and content availability change dynamically. In this paper, we rigorously study the achievable streaming capacity of large-scale P2P VoD systems with sparse connectivity among peers, and investigate simple and decentralized P2P control strategies that can provably achieve close-to-optimal streaming capacity. We first focus on a single streaming channel. We show that a close-to-optimal streaming rate can be asymptotically achieved for all peers with high probability as the number of peers N increases, by assigning each peer a random set of Θ(log N) neighbors and using a uniform rate-allocation algorithm. Further, the tracker does not need to obtain detailed knowledge of which chunks each peer caches, and hence incurs low overhead. We then study multiple streaming channels where peers watching one channel may help in another channel with insufficient upload bandwidth. We propose a simple random cache-placement strategy, and show that a close-to-optimal streaming capacity region for all channels can be attained with high probability, again with only Θ(log N) per-peer neighbors. These results provide important insights into the dynamics of large-scale P2P VoD systems, which will be useful for guiding the design of improved P2P control protocols.

Developing scheduling mechanisms that can simultaneously achieve throughput optimality and good delay performance often require solving the Maximum Independent Weighted Set (MWIS) problem. However, under most realistic network settings, the MWIS problem can be shown to be NP-hard. In non-fading environments, low-complexity scheduling algorithms have been provided that converge either to the MWIS solution in time or to a solution that achieves at least a provable fraction of the achievable throughput. However, in more practical systems the channel conditions can vary at faster time-scales than convergence occurs in these lower-complexity algorithms. Hence, these algorithms cannot take advantage of the opportunistic gain, and may no longer guarantee good performance. In this paper, we propose a low-complexity scheduling scheme that performs provably well under fading channels and is amenable to implement in a distributed manner. To the best of our knowledge, this is the first scheduling scheme under fading environments that requires only local information, has a low complexity that grows logarithmically with the network size, and achieves provable performance guarantees (which is arbitrarily close to that of the well-known centralized Greedy Maximal Scheduler). Through simulations we verify that both the throughput and the delay under our proposed distributed scheduling scheme are close to that of the optimal solution to MWIS. Further, we implement a preliminary version of our algorithm in a testbed by modifying the existing IEEE 802.11 DCF. The preliminary experiment results show that our implementation successfully accounts for wireless fading, and attains the opportunistic gains in practice, and hence substantially outperforms IEEE 802.11 DCF.

Microgrids represent an emerging paradigm of future electric power systems that can utilize both distributed and centralized generations. Two recent trends in microgrids are the integration of local renewable energy sources (such as wind farms) and the use of co-generation (i.e., to supply both electricity and heat). However, these trends also bring unprecedented challenges to the design of intelligent control strategies for microgrids. Traditional generation scheduling paradigms rely on perfect prediction of future electricity supply and demand. They are no longer applicable to microgrids with unpredictable renewable energy supply and with co-generation (that needs to consider both electricity and heat demand). In this paper, we study online algorithms for the microgrid generation scheduling problem with intermittent renewable energy sources and co-generation, with the goal of maximizing the cost-savings with local generation. Based on the insights from the structure of the offline optimal solution, we propose a class of competitive online algorithms, called CHASE (Competitive Heuristic Algorithm for Scheduling Energy-generation), that track the offline optimal in an online fashion. Under typical settings, we show that CHASE achieves the best competitive ratio among all deterministic online algorithms, and the ratio is no larger than a small constant 3. We also extend our algorithms to intelligently leverage on limited prediction of the future, such as near-term demand or wind forecast. By extensive empirical evaluations using real-world traces, we show that our proposed algorithms can achieve near offline-optimal performance. In a representative scenario, CHASE leads to around 20% cost reduction with no future look-ahead, and the cost reduction increases with the future look-ahead window.

In this paper, we study the queue-overflow probability of wireless scheduling algorithms. In wireless networks operated under queue-length-based scheduling algorithms, there often exists a tight coupling between the service-rate process, the system backlog process, the arrival process, and the stochastic process governing channel variations. Although one can use sample-path large-deviation techniques to form an estimate of the queue-overflow probability, the formulation leads to a difficult multidimensional calculus-of-variations problem. In this paper, we present a new technique to address this complexity issue. Using ideas from the Lyapunov function approach in control theory, this technique maps the complex multidimensional calculus-of-variations problem to a 1-D calculus-of-variations problem, and the latter is often much easier to solve. Further, under appropriate conditions, we show that when a scheduling algorithm minimizes the drift of a Lyapunov function at each point of every fluid sample path, the algorithm will be optimal in the sense that it maximizes the asymptotic decay rate of the probability that the Lyapunov function value exceeds a given threshold. We believe that these results can potentially be used to study the queue-overflow probability of a large class of wireless scheduling algorithms and to design new scheduling algorithms with optimal overflow probabilities.

Quantifying the end-to-end delay performance in multihop wireless networks is a well-known challenging problem. In this paper, we propose a new joint congestion control and scheduling algorithm for multihop wireless networks with fixed-route flows operated under a general interference model with interference degree K. Our proposed algorithm not only achieves a provable throughput guarantee (which is close to at least 1/K of the system capacity region), but also leads to explicit upper bounds on the end-to-end delay of every flow. Our end-to-end delay and throughput bounds are in simple and closed forms, and they explicitly quantify the tradeoff between throughput and delay of every flow. Furthermore, the per-flow end-to-end delay bound increases linearly with the number of hops that the flow passes through, which is order-optimal with respect to the number of hops. Unlike traditional solutions based on the back-pressure algorithm, our proposed algorithm combines window-based flow control with a new rate-based distributed scheduling algorithm. A key contribution of our work is to use a novel stochastic dominance approach to bound the corresponding per-flow throughput and delay, which otherwise are often intractable in these types of systems. Our proposed algorithm is fully distributed and requires a low per-node complexity that does not increase with the network size. Hence, it can be easily implemented in practice.

In this paper, we investigate the connectivity for large-scale clustered wireless sensor and ad hoc networks. We study the effect of mobility on the critical transmission range for asymptotic connectivity ink-hop clustered networks and compare to existing results on nonclustered stationary networks. By introducingk-hop clustering, any packet from a cluster member can reach a cluster head withinkhops, and thus the transmission delay is bounded as Θ(1) for any finitek. We first characterize the critical transmission range for connectivity in mobilek-hop clustered networks where all nodes move under either the random walk mobility model with nontrivial velocity or the i.i.d. mobility model. By the term nontrivial velocity, we mean that the velocity of a nodevis ω(r(n)), wherer(n) is the transmission range of the node. We then compare with the critical transmission range for stationaryk-hop clustered networks. In addition, the critical number of neighbors is studied in a parallel manner for both stationary and mobile networks. We also study the transmission power versus delay tradeoff and the average energy consumption per flow among different types of networks. We show that random walk mobility with nontrivial velocities increases connectivity ink-hop clustered networks, and thus significantly decreases the energy consumption and improves the power-delay tradeoff. The decrease of energy consumption per flow is shown to be Θ([(logn)/(nd)]) in clustered networks. These results provide insights on network design and fundamental guidelines on building a large-scale wireless network.

We study the multicast capacity under a network model featuring both node's mobility and infrastructure support. Combinations between mobility and infrastructure, as well as multicast transmission and infrastructure, have already been shown effective ways to increase capacity. In this work, we jointly consider the impact of the above three factors on network capacity. We assume that m static base stations and n mobile users are placed in an ad hoc network, of which the area scales with n as f2(n). A general mobility model is adopted, such that each user moves within a bounded distance from its homepoint with an arbitrary pattern. In addition, each mobile node serves as the source of a multicast transmission, which results in a total number of n multicast transmissions. We focus on the situations that base stations actually benefit the capacity, and prove that multicast capacity of mobile hybrid network falls into three regimes. For each regime, matching upper and lower bounds are derived.

In this paper, we study the problem of link scheduling for multi-hop wireless networks with per-flow delay constraints. Specifically, we are interested in algorithms that maximize the asymptotic decay-rate of the probability with which the maximum end-to-end backlog among all flows exceeds a threshold, as the threshold becomes large. We provide both positive and negative results in this direction. By minimizing the drift of the maximum end-to-end backlog in the converge-cast on a tree, we design an algorithm, Largest-Weight-First(LWF), that achieves the optimal asymptotic decay-rate for the overflow probability of the maximum end-to-end backlog as the threshold becomes large. However, such a drift minimization algorithm may not exist for general networks. We provide an example in which no algorithm can minimize the drift of the maximum end-to-end backlog. Finally, we simulate the LWF algorithm together with a well known algorithm (the back-pressure algorithm) and a large-deviations optimal algorithm in terms of the sum-queue (the P-TREE algorithm) in converge-cast networks. Our simulation shows that our algorithm significantly performs better not only in terms of asymptotic decay-rate, but also in terms of the actual overflow probability.

We consider the problem of designing a joint congestion control and scheduling algorithm for multihop wireless networks. The goal is to maximize the total utility and achieve low end-to-end delay simultaneously. Assume that there are M flows inside the network, and each flow m has a fixed route with Hmhops. Further, the network operates under the one-hop interference constraint. We develop a new congestion control and scheduling algorithm that combines a window-based flow control algorithm and a new distributed rate-based scheduling algorithm. For any ϵ, ϵm∈ (0, 1), by appropriately choosing the number of backoff mini-slots for the scheduling algorithm and the window-size of flow m, our proposed algorithm can guarantee that each flow m achieves throughput no smaller than rm(1 - ϵ)(1 - ϵm), where the total utility of the rate allocation vector r⃗ = [rm] is no smaller than the total utility of any rate vector within half of the capacity region. Furthermore, the end-to-end delay of flow m can be upper bounded by Hm/(rm(1 - ϵ)ϵm). Since a flow-m packet requires at least Hmtime slots to reach the destination, the order of the per-flow delay upper bound is optimal with respect to the number of hops. To the best of our knowledge, this is the first fully-distributed joint congestion-control and scheduling algorithm that can guarantee order-optimal per-flow end-to-end delay and utilize close-to-half of the system capacity under the one-hop interference constraint. The throughput and delay bounds are proved by a novel stochastic dominance approach, which could be of independent value and be extended to general interference constraints. Our algorithm can be easily implemented in practice with a low per-node complexity that does not increase with the network size.

We consider the problem of link scheduling for efficient convergecast in a wireless system. While there have been many results on scheduling algorithms that attain the maximum possible throughput in such a system, there have been few results that provide scheduling algorithms that are optimal in terms of some quality-of-service metric such as the probability that the end-to-end buffer usage exceeds a large threshold. Using a large deviations framework, we design a novel and low complexity algorithm that attains the optimal asymptotic decay rate for the overflow probability of the sum-queue (i.e. the total queue backlog in the entire system) as the overflow threshold becomes large. Simulations show that this algorithm has better performance than well known algorithms such as the standard back-pressure algorithm and the multihop version of greedy maximal matching (combined with back-pressure). Our proposed algorithm performs better not only in terms of the asymptotic decay rate at large overflow thresholds, but also in terms of the actual probability of overflow for practical range of overflow thresholds.

Peer-to-Peer (P2P) streaming technologies can take advantage of the upload capacity of clients, and hence can scale to large content distribution networks with lower cost. A fundamental question for P2P streaming systems is the maximum streaming rate that all users can sustain. Prior works have studied the optimal streaming rate for a complete network, where every peer is assumed to communicate with all other peers. This is however an impractical assumption in real systems. In this paper, we are interested in the achievable streaming rate when each peer can only connect to a small number of neighbors. We show that even with a random peer selection algorithm and uniform rate allocation, as long as each peer maintains Ω(log N) downstream neighbors, where N is the total number of peers in the system, the system can asymptotically achieve a streaming rate that is close to the optimal streaming rate of a complete network.We then extend our analysis to multi-channel P2P networks, and we study the scenario where “helpers” from channels with excessive upload capacity can help peers in channels with insufficient upload capacity. We show that by letting each peer select Ω(log N) neighbors randomly from either the peers in the same channel or from the helpers, we can achieve a close-to-optimal streaming capacity region. Simulation results are provided to verify our analysis.

Multimedia streaming applications have stringent Quality-of-Service (QoS) requirements. Typically, each packet is associated with a packet delivery deadline. This work models and considers streaming broadcast of stored video over the downlink of a single cell. We first generalize the existing class of immediately-decodable network coding (IDNC) schemes to take into account the deadline constraints. The performance analysis of IDNC schemes are significantly complicated by the packet deadline constraints (from the application layer) and the immediate-decodability requirement (from the network layer). Despite this difficulty, we prove that for independent channels, the IDNC schemes are asymptotically throughput-optimal subject to the deadline constraints when there are no more than three users and when the video file size is sufficiently large. The deadline-constrained throughput gain of IDNC schemes over non-coding scheme is also explicitly quantified. Numerical results show that IDNC schemes strictly outperform the non-coding scheme not only in the asymptotic regime of large files but also for small files. Our results show that the IDNC schemes do not suffer from the substantial decoding delay that is inherent to existing generation-based network coding protocols.

In wireless sensor networks (WSNs), asynchronous sleep-wake scheduling protocols can be used to significantly reduce energy consumption without incurring the communication overhead for clock synchronization needed for synchronous sleep-wake scheduling protocols. However, these savings could come at a significant cost in delay performance. Recently, researchers have attempted to exploit the inherent broadcast nature of the wireless medium to reduce this delay with virtually no additional energy cost. These schemes are called “anycasting,” where each sensor node forwards the packet to the first node that wakes up among a set of candidate next-hop nodes. In this paper, we develop a delay-optimal anycasting scheme under periodic sleep-wake patterns. Our solution is computationally simple and fully distributed. Furthermore, we show that periodic sleep-wake patterns result in the smallest delay among all wake-up patterns under given energy constraints. Simulation results illustrate the benefit of our proposed schemes over the state of the art.

Network utility maximization has been widely used to model resource allocation and network architectures. However, in practice, often it cannot be solved optimally due to complexity reasons. Thus motivated, we address the following two questions in this paper: 1) Can suboptimal utility maximization maintain queue stability? 2) Can underoptimization of utility objective function in fact benefit other network design objectives? We quantify the following intuition: A resource allocation that is suboptimal with respect to a utility maximization formulation maintains maximum flow-level stability when the utility gap is sufficiently small and information delay is bounded, and it can still provide a guaranteed size of stability region otherwise. Utility-suboptimal rate allocation can also enhance other network performance metrics, e.g., it may reduce link saturation. These results provide a theoretical support for turning attention from optimal but complex solutions of network optimization to those that are simple even though suboptimal.

Multimedia streaming applications have stringent QoS requirements. Typically each packet is associated with a packet delivery deadline. This work models and considers real-time streaming broadcast for stored-video over the downlink of a single cell. The broadcast capacity of the system subject to deadline constraints are derived for both uncoded and coded wireless broadcast schemes. Even under the deadline requirements, it is shown in this work that network coding is asymptotically throughput-optimal and can strictly outperform the best non-coding policy by analytically quantifying the optimal capacity when the file size is sufficiently large. A simple network coding policy is also proposed that achieves the asymptotic capacity while maintaining finite transmission delay (queueing + decoding delay). A new temporal-queue-length-based Lyapunov function is used to prove the optimality of this policy. Simulation shows that the simple coding policy outperforms the best non-coding policies even for broadcasting files of small sizes.

While there has been much progress in designing backpressure based stabilizing algorithms for multihop wireless networks, end-to-end performance (e.g., end-to-end buffer usage) results have not been as forthcoming. In this paper, we study the end-to-end buffer usage (sum of buffer utilization along a flow path) over a network with general topology and with fixed, loop-free routes using a large-deviations approach. We first derive bounds on the best performance that any scheduling algorithm can achieve. Based on the intuition from the bounds, we propose a class of (backpressure-like) scheduling algorithms called ¿ß-algorithms. We show that the parameters ¿ and ß can be chosen such that the system under the ¿ß-algorithm performs arbitrarily closely to the best possible scheduler (formally the decay rate function for end-to-end buffer overflow is shown to be arbitrarily close to optimal in the large-buffer regime). We also develop variants which have the same asymptotic optimality property, and also provide good performance in the small-buffer regime. Our results are substantiated using both analysis and simulation.

In this paper, we are interested in wireless scheduling algorithms for the downlink of a single cell that can minimize the queue-overflow probability. Specifically, in a large-deviation setting, we are interested in algorithms that maximize the asymptotic decay rate of the queue-overflow probability, as the queue-overflow threshold approaches infinity. We first derive an upper bound on the decay rate of the queue-overflow probability over all scheduling policies. We then focus on a class of scheduling algorithms collectively referred to as the “α-algorithms.” For a given α ≥ 1, the α-algorithm picks the user for service at each time that has the largest product of the transmission rate multiplied by the backlog raised to the power α. We show that when the overflow metric is appropriately modified, the minimum-cost-to-overflow under the α-algorithm can be achieved by a simple linear path, and it can be written as the solution of a vector-optimization problem. Using this structural property, we then show that when α approaches infinity, the α-algorithms asymptotically achieve the largest decay rate of the queue-overflow probability. Finally, this result enables us to design scheduling algorithms that are both close to optimal in terms of the asymptotic decay rate of the overflow probability and empirically shown to maintain small queue-overflow probabilities over queue-length ranges of practical interest.

In wireless sensor networks, asynchronous sleep-wake scheduling protocols can significantly reduce energy consumption without incurring the communication overhead for clock synchronization used in typical sleep-wake scheduling protocols. However, the savings could come at a significant cost in delay performance. Recently, researchers have attempted to exploit the inherent broadcast nature of the wireless medium to reduce this delay with virtually no additional energy cost. These schemes are called "anycasting," where each sensor node forwards the packet to the first node that wakes up among a set of candidate next-hop nodes. In this paper, we develop a delay-optimal anycasting scheme under periodic sleep-wake patterns. Our solution is computationally simple and fully distributed. We show that periodic sleep-wake patterns result in the smallest delay among all wake-up patterns under given energy constraints. Simulation results illustrate the benefit of our proposed schemes over the state-of-the art.

In this paper, we develop a fast resource allocation algorithm that takes advantage of intra-session network coding. The algorithm maximizes the total utility of multiple unicast (or multicast) sessions subject to capacity constraints, where packets are coded within each session. Our solution is a primal solution that does not use duality or congestion prices. Thus, it does not require building up queues to achieve the optimal resource allocation. Hence, the queueing delay of the packets can be tightly controlled. The existing primal solution in the literature requires a separate graph-theoretic algorithm to find the min-cut of each session, whose complexity grows quadratically with the total number of nodes. In contrast, we provide a new coded-feedback approach whose complexity grows only linearly with the total number of nodes. More explicitly, by letting the ACK/feedback packets on the return paths also carry coding coefficients as does the forward coded traffic, key network information can be obtained more efficiently, which leads to a fast resource allocation scheme fully integrated with the network coding operation.

In this paper we investigate the connectivity for large-scale clustered wireless sensor and ad hoc networks. We study the effect of mobility on the critical transmission range for asymptotic connectivity in k-hop clustered networks, and compare to existing results on non-clustered stationary networks. By introducing k-hop clustering, any packet from a cluster member can reach a cluster head within k hops, and thus the transmission delay is bounded as Θ(1) for any finite k. We first characterize the critical transmission range for connectivity in mobile k-hop clustered networks where all nodes move under either the random walk mobility model with non-trivial velocity or the i.i.d. mobility model. By the term non-trivial velocity, we mean that the velocity of nodes v is Θ(1). We then compare with the critical transmission range for stationary k-hop clustered networks. We also study the transmission power versus delay trade-off and the average energy consumption per flow among different types of networks. We show that random walk mobility with non-trivial velocity increases connectivity in k-hop clustered networks, and thus significantly decreases the energy consumption and improves the power-delay trade-off. The decrease of energy consumption per flow is shown to be Θ(logn/nd}) in clustered networks. These results provide insights on network design and fundamental guidelines on building a large-scale wireless network.

In this paper, we characterize the performance of an important class of scheduling schemes, called greedy maximal scheduling (GMS), for multi-hop wireless networks. While a lower bound on the throughput performance of GMS is relatively well-known in the simple node-exclusive interference model, it has not been thoroughly explored in the more general K-hop interference model. Moreover, empirical observations suggest that the known bounds are quite loose, and that the performance of GMS is often close to optimal. In this paper, we provide a number of new analytic results characterizing the performance limits of GMS. We first provide an equivalent characterization of the efficiency ratio of GMS through a topological property called the local-pooling factor of the network graph. We then develop an iterative procedure to estimate the local-pooling factor under a large class of network topologies and interference models. We use these results to study the worst-case efficiency ratio of GMS on two classes of network topologies. First, we show how these results can be applied to tree networks to prove that GMS achieves the full capacity region in tree networks under the K-hop interference model. Second, we show that the worst-case efficiency ratio of GMS in geometric network graphs is between 1/6 and 1/3.

Sleep-wake scheduling is an effective mechanism to prolong the lifetime of energy-constrained wireless sensor networks. However, it incurs an additional delay for packet delivery when each node needs to wait for its next-hop relay node to wake up, which could be unacceptable for delay-sensitive applications. Prior work in the literature has proposed to reduce this delay using anycast, where each node opportunistically selects the first neighboring node that wakes up among multiple candidate nodes. In this paper, we study the joint control problem of how to optimally control the sleep-wake schedule, the anycast candidate set of next-hop neighbors, and anycast priorities, to maximize the network lifetime subject to a constraint on the expected end-to-end delay. We provide an efficient solution to this joint control problem. Our numerical results indicate that the proposed solution can substantially outperform prior heuristic solutions in the literature, especially under the practical scenarios where there are obstructions in the coverage area of the wireless sensor network.

Not too bad. A rate allocation that is suboptimal with respect to a utility maximization formulation still maintains the maximum flow-level stability when the utility gap is sufficiently small, and provides a minimum size of stability region otherwise. Utility-suboptimal allocation may also enhance other network performance metrics, e.g., it may increase network throughput and reduce link saturation. Quantifying these intuitions, this paper provides a theoretical support for turning attention from optimal but complex solutions of network optimization to those that are simple even though suboptimal.

In this paper, we are interested in the connection-level stability of a network employing congestion control. In particular, we study how the stability region of the network (i.e., the set of offered loads for which the number of active users in the network remains finite) is affected by congestion control. Previous works in the literature typically adopt a time-scale separation assumption, which assumes that, whenever the number of users in the system changes, the data rates of the users are adjusted instantaneously to the optimal and fair rate allocation. Under this assumption, it has been shown that such rate assignment policies can achieve the largest possible stability region. In this paper, this time-scale separation assumption is removed and it is shown that the largest possible stability region can still be achieved by a large class of control algorithms. A second assumption often made in prior work is that the packets of a source (or user) are offered to each link along its path instantaneously, rather than passing through one queue at a time. We show that connection-level stability is again maintained when this assumption is removed, provided that a back-pressure scheduling algorithm is used jointly with the appropriate congestion controller.

We consider the problem of distributed scheduling in wireless networks. We present two different algorithms whose performance is arbitrarily close to that of maximal schedules, but which require low complexity due to the fact that they do not necessarily attempt to find maximal schedules. The first algorithm requires each link to collect local queue-length information in its neighborhood, and its complexity is independent of the size and topology of the network. The second algorithm is presented for the node-exclusive interference model, does not require nodes to collect queue-length information even in their local neighborhoods, and its complexity depends only on the maximum node degree in the network.

In this work, we study the problem of minimizing the total power consumption in a multi-hop wireless network subject to a given offered load. It is well-known that the total power consumption of multi-hop wireless networks can be substantially reduced by jointly optimizing power control, link scheduling, and routing. However, the known optimal cross-layer solution to this problem is centralized, and with high computational complexity. In this paper, we develop a low-complexity and distributed algorithm that is provably power-efficient. In particular, under the node exclusive interference model, we can show that the total power consumption of our algorithm is at most twice as large as the power consumption of the optimal (but centralized and complex) algorithm. Our algorithm is not only the first such distributed solution with provable performance bound, but its power-efficiency ratio is also tighter than that of another sub-optimal centralized algorithm in the literature.

The capacity of ad hoc wireless networks can be substantially increased by equipping each network node with multiple radio interfaces that can operate on multiple non-overlapping channels. However, new scheduling, channel-assignment, and routing algorithms are required to fully utilize the increased bandwidth in multi-channel multi-radio ad hoc networks. In this paper, we develop a fully distributed algorithm that jointly solves the channel-assignment, scheduling and routing problem. Our algorithm is an online algorithm, i.e., it does not require prior information on the offered load to the network, and can adapt automatically to the changes in the network topology and offered load. We show that our algorithm is provably efficient. That is, even compared with the optimal centralized and offline algorithm, our proposed distributed algorithm can achieve a provable fraction of the maximum system capacity. Further, the achievable fraction that we can guarantee is larger than that of some other comparable algorithms in the literature.

Internet distance prediction gives pair-wise latency information with limited measurements. Recent studies have revealed that the quality of existing prediction mechanisms from the application perspective is short of satisfactory. In this paper, we explore the root causes and remedies for this problem. Our experience with different landmark selection schemes shows that although selecting nearby landmarks can increase the prediction accuracy for short distances, it can cause the prediction accuracy for longer distances to degrade. Such uneven prediction quality significantly impacts application performance. Instead of trying to select the landmark nodes in some "intelligent" fashion, we propose a hierarchical prediction approach with straightforward landmark selection. Hierarchical prediction utilizes multiple coordinate sets at multiple distance scales, with the "right" scale being chosen for prediction each time. Experiments with Internet measurement datasets show that this hierarchical approach is extremely promising for increasing the accuracy of network distance prediction.

Distance prediction algorithms use O(N) round trip time (RTT) measurements to predict the N2RTTs among N nodes. Distance prediction can be applied to improve the performance of a wide variety of Internet applications: for instance, to guide the selection of a download server from multiple replicas, or to guide the construction of overlay networks or multicast trees. Although the accuracy of existing prediction algorithms has been extensively compared using the relative prediction error metric, their impact on applications has not been systematically studied. In this paper, we consider distance prediction algorithms from an application's perspective to answer the following questions: (1) Are existing prediction algorithms adequate for the applications? (2) Is there a significant performance difference between the different prediction algorithms, and which is the best from the application perspective? (3) How does the prediction error propagate to affect the user perceived application performance? (4) How can we address the fundamental limitation (i.e., inaccuracy) of distance prediction algorithms? We systematically experiment with three types of representative applications (overlay multicast, server selection, and overlay construction), three distance prediction algorithms (GNP, IDES, and the triangulated heuristic), and three real-world distance datasets (King, PlanetLab, and AMP). We find that, although using prediction can improve the performance of these applications, the achieved performance can be dramatically worse than the optimal case where the real distances are known. We formulate statistical models to explain this performance gap. In addition, we explore various techniques to improve the prediction accuracy and the performance of prediction-based applications. We find that selectively conducting a small number of measurements based on prediction-based screening is most effective.

This tutorial paper overviews recent developments in optimization-based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channel-aware) scheduling for cellular (single-hop) networks, where easily implementable myopic policies are shown to optimize system performance. We then describe key lessons learned and the main obstacles in extending the work to general resource allocation problems for multihop wireless networks. Towards this end, we show that a clean-slate optimization-based approach to the multihop resource allocation problem naturally results in a "loosely coupled" cross-layer solution. That is, the algorithms obtained map to different layers [transport, network, and medium access control/physical (MAC/PHY)] of the protocol stack, and are coupled through a limited amount of information being passed back and forth. It turns out that the optimal scheduling component at the MAC layer is very complex, and thus needs simpler (potentially imperfect) distributed solutions. We demonstrate how to use imperfect scheduling in the cross-layer framework and describe recently developed distributed algorithms along these lines. We conclude by describing a set of open research problems.

There has been significant recent interest within the networking research community to characterize the impact of mobility on the capacity and delay in mobile ad hoc networks. In this correspondence, the fundamental tradeoff between the capacity and delay for a mobile ad hoc network under the Brownian motion model is studied. It is shown that the two-hop relaying scheme proposed by Grossglauser and Tse (2001), while capable of achieving a per-node throughput of /spl Theta/(1), incurs an expected packet delay of /spl Omega/(logn//spl sigma//sub n//sup 2/), where /spl sigma//sub n//sup 2/ is the variance parameter of the Brownian motion model. It is then shown that an attempt to reduce the delay beyond this value results in the throughput dropping to its value under static settings. In particular, it is shown that under a large class of scheduling and relaying schemes, if the mean packet delay is O(n/sup /spl alpha////spl sigma//sub n//sup 2/), for any /spl alpha/<0, then the per-node throughput must be O(1//spl radic/n). This result is in sharp contrast to other results that have recently been reported in the literature.

In this paper, we study cross-layer design for rate control in multihop wireless networks. In our previous work, we have developed an optimal cross-layered rate control scheme that jointly computes both the rate allocation and the stabilizing schedule that controls the resources at the underlying layers. However, the scheduling component in this optimal cross-layered rate control scheme has to solve a complex global optimization problem at each time, and hence is too computationally expensive for online implementation. In this paper, we study how the performance of cross-layer rate control can be impacted if the network can only use an imperfect (and potentially distributed) scheduling component that is easier to implement. We study both the case when the number of users in the system is fixed and the case with dynamic arrivals and departures of the users, and we establish desirable results on the performance bounds of cross-layered rate control with imperfect scheduling. Compared with a layered approach that does not design rate control and scheduling together, our cross-layered approach has provably better performance bounds, and substantially outperforms the layered approach. The insights drawn from our analyses also enable us to design a fully distributed cross-layered rate control and scheduling algorithm for a restrictive interference model.

In this paper, we model and characterize the performance of multihop radio networks in the presence of energy constraints and design routing algorithms to optimally utilize the available energy. The energy model allows vastly different energy sources in heterogeneous environments. The proposed algorithm is shown to achieve a competitive ratio (i.e., the ratio of the performance of any off-line algorithm that has knowledge of all past and future packet arrivals to the performance of our online algorithm) that is asymptotically optimal with respect to the number of nodes in the network. The algorithm assumes no statistical information on packet arrivals and can easily be incorporated into existing routing frameworks (e.g., proactive or on-demand methodologies) in a distributed fashion. Simulation results confirm that the algorithm performs very well in terms of maximizing the throughput of an energy-constrained network. Further, a new threshold-based scheme is proposed to reduce the routing overhead while incurring only minimum performance degradation.

In this talk we study the issue of cross-layer design for rate control in multihop wireless networks. We have developed an optimal cross-layered rate control scheme that jointly computes both the rate allocation and the stabilizing schedule that controls the resources at the underlying layers. However, the scheduling component in this optimal cross-layered rate control scheme has to solve a complex global optimization problem at each time, and is hence too computationally expensive for online implementation. Thus, we study the impact on the performance of cross-layer rate control if the network can only use an imperfect (and potentially distributed) scheduling component that is easier to implement. We study scenarios with both fixed number of users as well as when the number of users change due to arrivals and departures in the system. In each case, we establish desirable results on the performance bounds of cross-layered rate control with imperfect scheduling. Our cross-layered approach provides provably better performance bounds when compared with a layered approach (that does not design rate control and scheduling together). The insights drawn from our analyses also enable us to design a fully distributed cross-layered rate control and scheduling algorithm under a restrictive interference model.

We show that when networks are large significant simplicity can be achieved for pricing-based control. We first consider a general loss network with Poisson arrivals and arbitrary holding time distributions. In dynamic pricing schemes, the network provider can charge different prices to the user according to the current utilization level of the network and also other factors. We show that when the system becomes large the performance (in terms of expected revenue) of an appropriately chosen static pricing scheme, whose price is independent of the current network utilization, will approach that of the optimal dynamic pricing scheme. Further, we show that under certain conditions, this static price is independent of the route that the flows take. We then extend the result to the case of dynamic routing, and show that the performance of an appropriately chosen static pricing scheme with bifurcation probability determined by average parameters can also approach that of the optimal dynamic routing scheme when the system is large. These results deepen our understanding of pricing-based network control. In particular, they provide us with the insight that, when the system is large, an appropriate pricing strategy based on the average network conditions (hence, slowly changing) can approach optimality.

In this paper, we propose an optimization based approach for quality of service routing in high-bandwidth networks. We view a network that employs QoS routing as an entity that distributively optimizes some global utility function. By solving the optimization problem, the network is driven to an efficient operating point. In earlier work, it has been shown that when the capacity of the network is large, this optimization takes on a simple form, and once the solution to this optimization problem is found, simple proportional QoS routing schemes will suffice. However, this optimization problem requires global information. We develop a distributed and adaptive algorithm that can efficiently solve the optimization online. Compared with existing QoS routing schemes, the proposed optimization based approach has the following advantages: (1) The computation and communication overhead can be greatly reduced without sacrificing performance; (2) The operating characteristics of the network can be analytically studied; and (3) The desired operating point can be tuned by choosing appropriate utility functions.