Blockchain leader-based protocols elect leaders for proposing the next block of transactions. Proposed blocks need to pass a validation routine in order to be added to the blockchain. Proposers may prioritize certain transactions based on their fees or accounts, which enables attackers to gain profits through block building, while simultaneously causing negative impacts on other users. A fair block selection follows a random selection of pending transactions among those that a proposer is aware of. We propose CFTO, a protocol that aims at encouraging fair block selection in a leader-based blockchain network while taking into account real network conditions, such as the network’s topology structure and the forwarding protocol. CFTO offers two main contributions. First, it provides incentives for acting honestly and diminishing malicious and dishonest nodes. To accomplish this, we use a reputation system, whereby each node is given a reputation score based on its actions. Second, it consists of an algorithm that evaluates the proposed blocks based on the zone structure of the network. Furthermore, we adapt the evaluation algorithm to fit the additional order constraints implied in Ethereum transaction ordering. We demonstrate the improved accuracy of CFTO in detecting fair blocks, in terms of increasing the probability of approving fair blocks and decreasing the probability of approving unfair blocks, by implementing experiments and comparing them with Helix (Yakira et al., 2021), a previously proposed consensus algorithm for fair block selection. As part of our experiments, we also compare certain features with those of previous studies.

Payment channel networks (PCNs) are a leading method to scale the transaction throughput in cryptocurrencies. Two participants can use a bidirectional payment channel for making multiple mutual payments without committing them to the blockchain. Opening a payment channel is a slow operation that involves an on-chain transaction locking a certain amount of funds. These aspects limit the number of channels that can be opened or maintained. Users may route payments through a multi-hop path and thus avoid opening and maintaining a channel for each new destination. Unlike regular networks, in PCNs capacity depends on the usage patterns and, moreover, channels may become unidirectional. Since payments often fail due to channel depletion, a protection scheme to overcome failures is of interest. We define the stopping time of a payment channel as the time at which the channel becomes depleted. We analyze the mean stopping time of a channel as well as that of a network with a set of channels and examine the stopping time of channels in particular topologies. We then propose a scheme for optimizing the capacity distribution among the channels in order to increase the minimal stopping time in the network. We conduct experiments and demonstrate the accuracy of our model and the efficiency of the proposed optimization scheme.

Blockchain leader-based protocols elect leaders for proposing the next block of transactions. Proposed blocks need to pass a validation routine in order to be added to the blockchain. Proposers may prioritize certain transactions based on their fees or accounts. A fair block selection follows a random selection of transactions among pending transactions that a proposer is aware of. The validators may only have partial knowledge of the network transactions making it challenging to validate the random selection. We propose a protocol to encourage fair block selection in a leader-based blockchain network. Our protocol offers two main contributions. First, suggesting an algorithm that evaluates the proposed blocks based on both their transactions’ issuance times and zone structure. Second, providing incentives for acting honestly and diminishing malicious and dishonest nodes. To accomplish this, we use a reputation system, whereby each node is given a reputation score based on its actions (i.e. latest proposals and evaluations). We demonstrate the improved accuracy of our protocol by implementing experiments based on Ethereum topology, comparing it with Helix [1], an existing consensus algorithm for a fair block selection.

Cloud operators require timely identification of Heavy Hitters (HH) and Hierarchical Heavy Hitters (HHH) for applications such as load balancing, traffic engineering, and attack mitigation. However, existing techniques are slow in detecting new heavy hitters. In this paper, we present the case for identifying heavy hitters throughsliding windows. Sliding windows are quicker and more accurate to detect new heavy hitters than current interval-based methods, but to date had no practical algorithms. Accordingly, we introduce, design, and analyze theMementofamily of sliding window algorithms for the HH and HHH problems in the single-device and network-wide settings. We use extensive evaluations to show that our single-device solutions are orders of magnitude faster than existing sliding window techniques and comparable in speed to state-of-the-art non-windowed sampling based technique. Furthermore, we exemplify our network-wide HHH detection capabilities on a realistic testbed. To that end, we implemented Memento as an open-source extension to the popular HAProxy cloud load-balancer. In our evaluations, using an HTTP flood by 50 subnets, our network-wide approach detected the new subnets faster and reduced the number of undetected flood requests by up to$37\times $compared to the alternatives.

Hash-based stateful load-balancers employ connection tracking to avoid per-connection-consistency (PCC) violations that lead to broken connections. In this paper, we propose Just Enough Tracking (JET), a new algorithmic framework that significantly reduces the size of the connection tracking tables for hash-based stateful load-balancers without increasing PCC violations.

Consistent hashing is a central building block in many networking applications, such as maintaining connection affinity of TCP flows. However, current consistent hashing solutions do not ensure full consistency under arbitrary changes or scale poorly in terms of memory footprint, update time and key lookup complexity. We present AnchorHash, a scalable and fully-consistent hashing algorithm. AnchorHash achieves high key lookup rate, low memory footprint and low update time. We formally establish its strong theoretical guarantees, and present an advanced implementation with a memory footprint of only a few bytes per resource. Moreover, evaluations indicate that AnchorHash scales on a single core to 100 million resources while still achieving a key lookup rate of more than 15 million keys per second.

Nowadays, the efficiency and even the feasibility of traditional load-balancing policies are challenged by the rapid growth of cloud infrastructure and the increasing levels of server heterogeneity. In such heterogeneous systems with many loadbalancers, traditional solutions, such as JSQ, incur a prohibitively large communication overhead and detrimental incast effects due to herd behavior. Alternative low-communication policies, such as JSQ(d) and the recently proposed JIQ, are either unstable or provide poor performance. We introduce the Local Shortest Queue (LSQ) family of load balancing algorithms. In these algorithms, each dispatcher maintains its own, local, and possibly outdated view of the server queue lengths, and keeps using JSQ on its local view. A small communication overhead is used infrequently to update this local view. We formally prove that as long as the error in these local estimates of the server queue lengths is bounded in expectation, the entire system is strongly stable. Finally, in simulations, we show how simple and stable LSQ policies exhibit appealing performance and significantly outperform existing low-communication policies, while using an equivalent communication budget. In particular, our simple policies often outperform even JSQ due to their reduction of herd behavior. We further show how, by relying on smart servers (i.e., advanced pull-based communication), we can further improve performance and lower communication overhead.

Cloud operators require real-time identification of Heavy Hitters (HH) and Hierarchical Heavy Hitters (HHH) for applications such as load balancing, traffic engineering, and attack mitigation. However, existing techniques are slow in detecting new heavy hitters.

Network providers now want to enable users to define their own flow priorities, and commercial devices already implement this ability. However, it has been shown that directly applying arbitrary user-defined priorities can fundamentally destabilize a network. In this paper, we show that it is possible to apply user-defined priorities while keeping the network stable. We introduce U-BP, a scalable approach that extends backpressure-based scheduling techniques to service user-defined flow priorities and rates while maintaining throughput optimality and strong network performance. We explain how our approach relies on a dual-layer scheme with an exponential convergence to requested priorities. We further prove analytically the network stability of our solution, and show how it achieves a strong performance for high-priority flows.

We present dRMT (disaggregated Reconfigurable Match-Action Table), a new architecture for programmable switches. dRMT overcomes two important restrictions of RMT, the predominant pipeline-based architecture for programmable switches: (1) table memory is local to an RMT pipeline stage, implying that memory not used by one stage cannot be reclaimed by another, and (2) RMT is hardwired to always sequentially execute matches followed by actions as packets traverse pipeline stages. We show that these restrictions make it difficult to execute programs efficiently on RMT.

We establish a network formation game for the Internet's autonomous system (AS) interconnection topology. The game includes different types of players, accounting for the heterogeneity of ASs in the Internet. In this game, the utility of a player depends on the network structure, e.g., the distances between nodes and the cost of links. Our model is versatile and can accommodate various configurations: whether monetary transfers are allowed, whether survivability requirements are imposed or not, and if so, whether failures are frequent or rare. We analyze static properties of the game as well as its dynamic evolution. We provide a dynamic analysis of topological quantities, and explain the prevalence of some “network motifs” in the Internet connectivity graph. We assess our predictions with real-world data.

Backpressure schemes are known to stabilize stochastic networks through the use of congestion gradients in routing and resource allocation decisions. Nonetheless, these schemes share a significant drawback, namely, the delay guarantees are obtained only in terms of average values. As a result, arbitrary packets may never reach their destination due to both the starvation and last-packet problems. These problems occur because in backpressure schemes, packet scheduling needs a subsequent stream of packets to produce the required congestion gradient for scheduling. To solve these problems, we define a starvation-free stability criterion that ensures a repeated evacuation of all network queues. Then, we introduce SF-BP, the first backpressure routing and resource allocation algorithm that is starvation-free stable. We further present stronger per-queue service guarantees and provide tools to enhance weak streams. We formally prove that our algorithm ensures that all packets reach their destination for wide families of networks. Finally, we verify our results by extensive simulations using challenging topologies as well as random static and dynamic topologies.

Coping with network failures has been recognized as an issue of major importance in terms of social security, stability, and prosperity. It has become clear that current networking standards fall short of coping with the complex challenge of surviving failures. The need to address this challenge has become a focal point of networking research. In particular, the concept of tunable survivability offers major performance improvements over traditional approaches. Indeed, while the traditional approach aims at providing full (100%) protection against network failures through disjoint paths, it was realized that this requirement is too restrictive in practice. Tunable survivability provides a quantitative measure for specifying the desired level (0%-100%) of survivability and offers flexibility in the choice of the routing paths. Previous work focused on the simpler class of “bottleneck” criteria, such as bandwidth. In this paper, we focus on the important and much more complex class of additive criteria, such as delay and cost. First, we establish some (in part, counter-intuitive) properties of the optimal solution. Then, we establish efficient algorithmic schemes for optimizing the level of survivability under additive end-to-end quality of service (QoS) bounds. Subsequently, through extensive simulations, we show that, at the price of negligible reduction in the level of survivability, a major improvement (up to a factor of 2) is obtained in terms of end-to-end QoS performance. Finally, we exploit the above findings in the context of a network design problem, in which, for a given investment budget, we aim to improve the survivability of the network links.

Hybrid switching combines a high-bandwidth optical circuit switch in parallel with a low-bandwidth electronic packet switch. It presents an appealing solution for scaling datacenter architectures. Unfortunately, it does not fit many traffic patterns produced by typical datacenter applications, and in particular the skewed traffic patterns that involve highly intensive one-to-many and many-to-one communications.

Network survivability has been recognized as an issue of major importance in terms of security, stability and prosperity. A crucial research problem in this context is the identification of suitable pairs of disjoint paths. Here, “disjointness” can be considered in terms of either nodes or links. Accordingly, several studies have focused on finding pairs of either link or node disjoint paths with a minimum sum of link weights. In this study, we investigate the gap between the optimal node-disjoint and link-disjoint solutions. Specifically, we formalize several optimization problems that aim at finding minimum-weight link-disjoint paths while restricting the number of its common nodes. We establish that some of these variants are computationally intractable, while for other variants we establish polynomial-time algorithmic solutions. Finally, through extensive simulations, we show that, by allowing link-disjoint paths share a few common nodes, a major improvement is obtained in terms of the quality (i.e., total weight) of the solution.

A fundamental capability of cloud computing is elasticity, i.e., the ability to dynamically change the amount of allocated resources. This is typically done by adjusting the number of Virtual Machines (VMs) running a service based on the current demand for that service. For large services, centralized management is impractical and distributed methods are employed. In such settings, no single component has full information on the overall demand and service quality, thus elasticity becomes a real challenge. We address this challenge by proposing a novel elasticity scheme that enables fully distributed management of large cloud services. Our scheme is based on three main components, namely, a task assignment policy, a VM scale-up policy and a VM scale-down policy. The task assignment policy strives to “pack” VMs while maintaining SLA requirements. The VM scale-up policy is based on local activation of new VMs and the VM scale-down policy is based on self-deactivation of VMs that are idle for some duration of time. Through simulations and an implementation we establish that our scheme quickly adapts to changes in job arrival rates and minimizes the number of active VMs so as to reduce the operational costs of the service, while adhering to strict SLA requirements.

Over the recent years we witness a massive growth of cloud usage, accelerated by new types of 'born-to-the-cloud' workloads. These new types of workloads are increasingly multi-component, dynamic and often present highly intensive communication patterns. Massive innovation of Data Center Network (DCN) technologies is required to support the demand, giving raise to new network topologies, new network control paradigms, and management models. One particularly promising technology candidate for improving the DCN efficiency is Optical Circuit Switching (OCS).

In the context of networking, research has focused on non-cooperative games, where the selfish agents cannot reach a binding agreement on the way they would share the infrastructure. Many approaches have been proposed for mitigating the typically inefficient operating points. However, in a growing number of networking scenarios, selfish agents are able to communicate and reach an agreement. Hence, the degradation of performance should be considered at an operating point of a cooperative game. Accordingly, our goal is to lay foundations for the application of the cooperative game theory to fundamental problems in networking. We explain our choice of the Nash bargaining scheme (NBS) as the solution concept, and introduce the price of selfishness (PoS), which considers the degradation of performance at the worst NBS. We focus on the fundamental load balancing game of routing over parallel links. First, we consider agents with identical performance objectives. We show that, while the price of anarchy (PoA) here can be large, through bargaining, all agents, and the system, strictly improve their performance. Interestingly, in a two-agent system or when all the agents have identical demands, we establish that they reach social optimality. We then consider agents with different performance objectives and demonstrate that the PoS and PoA can be unbounded, yet we explain why both measures are unsuitable. Accordingly, we introduce the price of heterogeneity (PoH), as an extension of the PoA. We establish an upper bound on the PoH and indicate its further motivation for bargaining. Finally, we discuss network design guidelines that follow from our findings.

Coping with network failures has become a major networking challenge. The concept of tunable survivability provides a quantitative measure for specifying any desired level (0%-100%) of survivability, thus offering flexibility in the routing choice. Previous works focused on implementing this concept on unicast transmissions. However, vital network information is often broadcast via spanning trees. Accordingly, in this study, we investigate the application of tunable survivability for efficient maintenance of spanning trees under the presence of failures. We establish efficient algorithmic schemes for optimizing the level of survivability under various QoS requirements. In addition, we derive theoretical bounds on the number of required trees for maximum survivability. Finally, through extensive simulations, we demonstrate the effectiveness of the tunable survivability concept in the construction of spanning trees. Most notably, we show that, typically, negligible reduction in the level of survivability results in major improvement in the QoS performance of the resulting spanning trees.

Load balancing of large distributed server systems is a complex optimization problem of critical importance in cloud systems and data centers. Existing schedulers often incur a high communication overhead when collecting the data required to make scheduling decisions, hence delaying job requests on their way to the executing servers. We propose a novel scheme that incurs no communication overhead between the users and the servers upon job arrival, thus removing any scheduling overhead from the job's critical path. Our approach is based on creating several replicas of each job and sending each replica to a different server. Upon the arrival of a replica to the head of the queue at its server, the latter signals the servers holding replicas of that job, so as to remove them from their queues. We show, through analysis and simulations, that this scheme significantly improves the expected queuing overhead over traditional schemes under various load conditions and different job length distributions. In addition, we show that our scheme remains efficient even when the inter-server signal propagation delay is significant (relative to the job's execution time). We provide a heuristic solution to the performance degradation that occurs in such cases and show, by simulations, that it efficiently mitigates the detrimental effect of propagation delays.

Stackable Routers, i.e. a class of independent routing units operating together as a single router, constitute an affordable scalable approach for coping with the growing networking requirements of organizations. In this study, we investigate several design problems of stackable routers and develop novel schemes for improving their performance. First, we formalize a mathematical model for optimizing the network topology in terms of throughput and delay, while obeying constraints in the number of ports of each internal routing unit. We then consider the problem of minimizing the diameter of the interconnection topology, as a measure of maximum delay, and establish efficient near-to optimal (explicit) topologies. Furthermore, we also consider the problem of maximizing the throughput of a stackable router. We show its hardness and derive bounds for the optimal solution. While, traditionally, the different routing units of a stackable router are linked together in a ring topology, through simulations we show that a major improvement in the diameter of stackable routers can be accomplished even through the employment of randomly-generated topologies. Finally, we investigate the basic problem of constructing a feasible stackable router and establish some fundamental properties of the required structure of the routing units.

Resource allocation and management in Cloud Computing is a very complex task. This is mainly due to the scale of the cloud and the number of services deployed in it. Since cloud users and service providers are given access to supercomputerlevel resources, their effect over the cloud's overall performance is greater than ever. This raises multiple research questions related to the management and performance of cloud computing systems in light of the end-users selfishness. In this work we specifically study the overall performance when selfish service providers may split work between the (shared) cloud and private resources. The size of modern data center and the number of service housed in it calls for fully distributed management solutions. We propose task assignment policies that are specifically adequate for large-scale distributed systems, and show that they provide new capabilities in improving system performance. In particular, we develop new resource allocation algorithms that converge to a working point that balances the end-user experience with the operational costs of leasing resources from the cloud provider.

We establish a network formation game for the Internet's Autonomous System (AS) interconnection topology. The game includes different types of players, accounting for the heterogeneity of ASs in the Internet. We incorporate reliability considerations in the player's utility function, and analyze static properties of the game as well as its dynamic evolution. We provide dynamic analysis of topological quantities, and explain the prevalence of some “network motifs” in the Internet graph. We assess our predictions with real-world data.

We consider the problem of detecting an epidemic in a population where individual diagnoses are extremely noisy. We show that exclusively local, approximate knowledge of the contact network suffices to accurately detect the epidemic. The motivation for this problem is the plethora of examples (influenza strains in humans, or computer viruses in smartphones, etc.) where reliable diagnoses are scarce, but noisy data plentiful. In flu or phone-viruses, exceedingly few infected people/phones are professionally diagnosed (only a small fraction go to a doctor) but less reliable secondary signatures (e.g., people staying home, or greater-than-typical upload activity) are more readily available.

There is a rich recent literature on information-theoretically secure communication at the physical layer of wireless networks, where secret communication between a single transmitter and receiver has been studied extensively. In this paper, we consider how single-hop physical layer security techniques can be extended to multi-hop wireless networks. We show that guaranteed security can be achieved in multi-hop networks by augmenting physical layer security techniques, such as cooperative jamming, with the higher layer network mechanisms, such as routing. Specifically, we consider the secure minimum energy routing problem, in which the objective is to compute a minimum energy path between two network nodes subject to constraints on the end-to-end communication secrecy and goodput over the path. This problem is formulated as a constrained optimization of transmission power and link selection, which is proved to be NP-hard. Nevertheless, we show that efficient algorithms exist to compute both exact and approximate solutions for the problem. In particular, we develop an exact solution of pseudo-polynomial complexity, as well as an ε-optimal approximation of polynomial complexity. Simulation results are also provided to show the utility of our algorithms and quantify their energy savings compared to a combination of (standard) security-agnostic minimum energy routing and physical layer security. In the simulated scenarios, we observe that, by jointly optimizing link selection at the network layer and cooperative jamming at the physical layer, our algorithms reduce the network energy consumption by half.

Contention among users utilizing a single shared resource arises in multiple contexts of computing and computer communications. We consider a setup in which users can split their work between a shared resource and a private resource. Unlike the private resource, which provides guaranteed performance, the performance of the shared resource is highly dependent on the usage pattern of other users, which in turn influences a user's decision if and to what extent to make use of the shared resource. The intrinsic relation between the utility that a user perceives from the shared resource and the usage pattern followed by other users gives rise to a noncooperative game, which we model and investigate. We show that the considered game admits a Nash equilibrium. Moreover, we show that this equilibrium is unique. We investigate the ratio between the worst Nash equilibrium and the social optimum, known as the “price of anarchy,” and show that, while in some cases of interest the Nash equilibrium coincides with a social optimum, in other cases the price of anarchy can be arbitrarily large. We demonstrate that, somewhat counterintuitively, exercising admission control to the shared resource may deteriorate its performance. Furthermore, we demonstrate that certain (heavy) users may “scare off” other, potentially large, communities of users. Accordingly, we propose a resource allocation scheme that addresses this problem and opens the shared resource to a wide range of user types.

Solving network flow problems is a fundamental component of traffic engineering and many communications applications, such as content delivery or multi-processor scheduling. While a rich body of work has addressed network flow problems in "deterministic networks" finding flows in "stochastic networks" where performance metrics like bandwidth and delay are uncertain and solely known by a probability distribution based on historical data, has received less attention. The work on stochastic networks has predominantly been directed to developing single-path routing algorithms, instead of addressing multi-path routing or flow problems. In this paper, we study constrained maximum flow problems in stochastic networks, where the delay and bandwidth of links are assumed to follow a log-concave probability distribution, which is the case for many distributions that could represent bandwidth and delay. We formulate the maximum-flow problem in such stochastic networks as a convex optimization problem, with a polynomial (in the input) number of variables. When an additional delay constraint is imposed, we show that the problem becomes NP-hard and we propose an approximation algorithm based on convex optimization. Furthermore, we develop a fast heuristic algorithm that, with a tuning parameter, is able to balance accuracy and speed. In a simulation-based evaluation of our algorithms in terms of success ratio, flow values, and running time, our heuristic is shown to give good results in a short running time.

We study the structure and evolution of the Internet's Autonomous System (AS) interconnection topology as a game with heterogeneous players. In this network formation game, the utility of a player depends on the network structure, e.g., the distances between nodes and the cost of links. We analyze static properties of the game, such as the prices of anarchy and stability and provide explicit results concerning the generated topologies. Furthermore, we discuss dynamic aspects, demonstrating linear convergence rate and showing that only a restricted subset of equilibria is feasible under realistic dynamics. We also consider the case where utility (or monetary) transfers are allowed between the players.

Coping with network failures has become a major networking challenge. The concept of tunable survivability provides a quantitative measure for specifying any desired level (0%-100%) of survivability, thus offering flexibility in the routing choice. Previous works focused on implementing this concept on unicast transmissions. However, vital network information is often broadcasted via spanning trees. Accordingly, in this study, we investigate the application of tunable survivability for efficient maintenance of spanning trees under the presence of failures. We establish efficient algorithmic schemes for optimizing the level of survivability under various QoS requirements. In addition, we derive theoretical bounds on the number of required trees for maximum survivability. Finally, through extensive simulations, we demonstrate the effectiveness of the tunable survivability concept in the construction of spanning trees. Most notably, we show that, typically, negligible reduction in the level of survivability results in major improvement in the QoS performance of the resulting spanning trees.

We study the performance of noncooperative networks in light of three major topology design considerations, namely the price of establishing a link, path delay, and path proneness to congestion, the latter being modeled through the “relaying extent” of the nodes. We analyze these considerations and the tradeoffs between them from a game-theoretic perspective, where each network element attempts to optimize its individual performance. We show that for all considered cases but one, the existence of a Nash equilibrium point is guaranteed. For the latter case, we indicate, by simulations, that practical scenarios tend to admit a Nash equilibrium. In addition, we demonstrate that the price of anarchy, i.e., the performance penalty incurred by noncooperative behavior, may be prohibitively large; yet, we also show that such games usually admit at least one Nash equilibrium that is system-wide optimal, i.e., their price of stability is 1. This finding suggests that a major improvement can be achieved by providing a central (“social”) agent with the ability to impose the initial configuration on the system.

Load balancing in large distributed server systems is a complex optimization problem of critical importance in cloud systems and data centers. Existing schedulers often incur a high overhead in communication when collecting the data required to make the scheduling decision, hence delaying the job request on its way to the executing server. We propose a novel scheme that incurs no communication overhead between the users and the servers upon job arrival, thus removing any scheduling overhead from the job's critical path. Our approach is based on creating several replicas of each job and sending each replica to a different server. Upon the arrival of a replica to the head of the queue at its server, the latter signals the servers holding replicas of that job, so as to remove them from their queues. We show, through analysis and simulations, that this scheme improves the expected queuing overhead over traditional schemes by a factor of 9 (or more) under various load conditions. In addition, we show that our scheme remains efficient even when the inter-server signal propagation delay is significant (relative to the job's execution time). We provide heuristic solutions to the performance degradation that occurs in such cases and show, by simulations, that they efficiently mitigate the detrimental effect of propagation delays. Finally, we demonstrate the efficiency of our proposed scheme in a real-world environment by implementing a load balancing system based on it, deploying the system on the Amazon Elastic Compute Cloud (EC2), and measuring its performance.

Coping with network failures has been recognized as an issue of major importance in terms of social security, stability and prosperity. It has become clear that current networking standards fall short of coping with the complex challenge of surviving failures. The need to address this challenge has become a focal point of networking research. In particular, the concept of tunable survivability offers major performance improvements over traditional approaches. Indeed, while the traditional approach is to provide full (100%) protection against network failures through disjoint paths, it was realized that this requirement is too restrictive in practice. Tunable survivability provides a quantitative measure for specifying the desired level (0%-100%) of survivability and offers flexibility in the choice of the routing paths. Previous work focused on the simpler class of “bottleneck” criteria, such as bandwidth. In this study, we focus on the important and much more complex class of additive criteria, such as delay and cost. First, we establish some (in part, counter-intuitive) properties of the optimal solution. Then, we establish efficient algorithmic schemes for optimizing the level of survivability under additive end-to-end QoS bounds. Subsequently, through extensive simulations, we show that, at the price of negligible reduction in the level of survivability, a major improvement (up to a factor of 2) is obtained in terms of end-to-end QoS performance. Finally, we exploit the above findings in the context of a network design problem, in which we need to best invest a given “budget” for improving the performance of the network links.

There is a rich recent literature on how to assist secure communication between a single transmitter and receiver at the physical layer of wireless networks through techniques such as cooperative jamming. In this paper, we consider how these single-hop physical layer security techniques can be extended to multi-hop wireless networks and show how to augment physical layer security techniques with higher layer network mechanisms such as coding and routing. Specifically, we consider the secure minimum energy routing problem, in which the objective is to compute a minimum energy path between two network nodes subject to constraints on the end-to-end communication secrecy and goodput over the path. This problem is formulated as a constrained optimization of transmission power and link selection, which is proved to be NP-hard. Nevertheless, we show that efficient algorithms exist to compute both exact and approximate solutions for the problem. In particular, we develop an exact solution of pseudo-polynomial complexity, as well as an o-optimal approximation of polynomial complexity. Simulation results are also provided to show the utility of our algorithms and quantify their energy savings compared to a combination of (standard) security-agnostic minimum energy routing and physical layer security. In the simulated scenarios, we observe that, by jointly optimizing link selection at the network layer and cooperative jamming at the physical layer, our algorithms reduce the network energy consumption by half.

Game theoretic models have been widely employed in many networking contexts. Research to date has mainly focused on non-cooperative networking games, where the selfish agents cannot reach a binding agreement on the way they would share the network infrastructure and the operating points are the Nash equilibria. These are typically inefficient, as manifested by large values of the Price of Anarchy (PoA). Many approaches have been proposed for mitigating this problem, however under the standing assumption of a non-cooperative game. In a growing number of networking scenarios it is possible for the selfish agents to communicate and reach an agreement, i.e., play a cooperative game. Therefore, the degradation of performance should be considered at an operating point that is a cooperative game solution. Accordingly, our goal is to lay foundations for the application of cooperative game theory to fundamental problems in networking. We explain our choice of the Nash Bargaining Scheme (NBS) as the solution concept, and we introduce the Price of Selfishness (PoS), which considers the degradation of performance at an NBS. We focus on the fundamental load balancing game of routing over parallel links. First, we study the classical scenario of agents that consider the same performance objectives. While the PoA here can be very large, we establish that, under plausible assumptions, the PoS attains its minimum value, i.e., through bargaining, the selfish agents reach social optimality. We then extend our study to consider the “heterogeneous” case, where agents may consider vastly different performance objectives. We demonstrate that the PoS and PoA can be unbounded, yet we explain why both measures may now be unsuitable. Accordingly, we introduce the Price of Heterogeneity (PoH), as a proper extension of the PoA. We establish an upper-bound on the PoH for a general class of heterogeneous performance objectives, and indicate that it provides incentives for bargaining also in this general case. We discuss network design guidelines that follow from our findings.

Cloud computing is an emerging paradigm in which tasks are assigned to a combination (“cloud”) of servers and devices, accessed over a network. Typically, the cloud constitutes an additional means of computation and a user can perform workload factoring, i.e., split its load between the cloud and its other resources. Based on empirical data, we demonstrate that there is an intrinsic relation between the “benefit” that a user perceives from the cloud and the usage pattern followed by other users. This gives rise to a non-cooperative game, which we model and investigate. We show that the considered game admits a Nash equilibrium. Moreover, we show that this equilibrium is unique. We investigate the “price of anarchy” of the game and show that, while in some cases of interest the Nash equilibrium coincides with a social optimum, in other cases the gap can be arbitrarily large. We show that, somewhat counter-intuitively, exercising admission control to the cloud may deteriorate its performance. Furthermore, we demonstrate that certain (heavy) users may “scare off” other, potentially large, communities of users. Accordingly, we propose a resource allocation scheme that addresses this problem and opens the cloud to a wide range of user types.

A major problem in wireless networks is coping with limited resources, such as bandwidth and energy. These issues become a major algorithmic challenge in view of the dynamic nature of the wireless domain. We consider in this paper the single-transmitter power assignment problem under time-varying channels, with the objective of maximizing the data throughput. It is assumed that the transmitter has a limited power budget, to be sequentially divided during the lifetime of the battery. We deviate from the classic work in this area, which leads to explicit “water-filling” solutions, by considering a realistic scenario where the channel state quality changes arbitrarily from one transmission to the other. The problem is accordingly tackled within the framework of competitive analysis, which allows for worst-case performance guarantees in setups with arbitrarily varying channel conditions. We address both a “discrete” case, where the transmitter can transmit only at a fixed power level, and a “continuous” case, where the transmitter can choose any power level out of a bounded interval. For both cases, we propose online power-allocation algorithms with proven worst-case performance bounds. In addition, we establish lower bounds on the worst-case performance of any online algorithm and show that our proposed algorithms are optimal.

The Internet has evolved towards a unique technology base for creating value-added services with worldwide connectivity. These services, enabled by the increasing bandwidth of access networks, result in new high-performance applications (e.g. e-health, high definition video streaming, network gaming etc.) To support and materialize the value of these emerging services, it is important for the operators to be able to provide some form of Quality of Service (QoS) assurance. This paper presents the main economic issues regarding the efficient provisioning of such services in inter-domain level and overviews some candidate economic mechanisms and game-theoretic tools that could be adopted.

Physical impairments, such as noise and signal distortions, negatively affect the quality of information transfer in optical networks. The effect of physical impairments predominantly augments with distance and bit rate of the signal to the point that it becomes detrimental to the information transfer. To reverse the effect of physical impairments, the signal needs to be regenerated at nodes that have regeneration capabilities. Regenerators are costly and are, therefore, usually only sparsely placed in the network, in which case it is referred to as a translucent network. This paper deals with two problems in translucent networks, namely: (1) how to incorporate impairment awareness in the routing algorithms, and (2) how many regenerators to place inside the network and where. We propose exact and heuristic algorithms for impairment-aware path selection and, through simulations, show that our heuristic TIARA is computationally efficient and performs very close to our exact algorithm EIARA. Subsequently, we propose a greedy algorithm for placing regenerators that, contrary to previous proposals, is suitable for multiple impairment metrics, has polynomial complexity for a single impairment metric, and is cheaper in terms of the number of regenerators needed.

There are two basic approaches to allocate protection resources for fast restoration. The first allocates resources upon the arrival of each connection request; yet, it incurs significant set-up time and is often capacity-inefficient. The second approach allocates protection resources during the network configuration phase; therefore, it needs to accommodate any possible arrival pattern of connection requests, hence potentially calling for a substantial over-provisioning of resources. However, in this study we establish the feasibility of this approach. Specifically, we consider a scheme that, during the network configuration phase, constructs an (additional) low-capacity backup network. Upon a failure, traffic is rerouted through a bypass in the backup network. We establish that, with proper design, backup networks induce feasible capacity overhead. We further impose several design requirements (e.g., hop-count limits) on backup networks and their induced bypasses, and prove that, commonly, they also incur minor overhead. Motivated by these findings, we design efficient algorithms for the construction of backup networks.

We consider the power control problem in a time-slotted wireless channel, shared by a finite number of mobiles that transmit to a common base station. The channel between each mobile and the base station is time varying, and the system objective is to maximize the overall data throughput. It is assumed that each transmitter has a limited power budget, to be sequentially divided during the lifetime of the battery. We deviate from the classic work in this area, by considering a realistic scenario where the channel quality of each mobile changes arbitrarily from one transmission to the other. Assuming first that each mobile is aware of the channel quality of all other mobiles, we propose an online power-allocation algorithm, and prove its optimality under mild assumptions. We then indicate how to implement the algorithm when only local state information is available, requiring minimal communication overhead. Notably, the competitive ratio of our algorithm (nearly) matches the one we previously obtained for the (much simpler) single-transmitter case [BLMNO09], albeit requiring significantly different algorithmic solutions.

A major problem in wireless networks is coping with limited resources, such as bandwidth and energy. These issues become a major algorithmic challenge in view of the dynamic nature of the wireless domain. We consider in this paper the single-transmitter power assignment problem under time-varying channels, with the objective of maximizing the data throughput. It is assumed that the transmitter has a limited power budget, to be sequentially divided during the lifetime of the battery. We deviate from the classic work in this area, which leads to explicit "water-filling" solutions, by considering a realistic scenario where the channel state quality changes arbitrarily from one transmission to the other. The problem is accordingly tackled within the framework of competitive analysis, which allows for worst case performance guarantees in setups with arbitrarily varying channel conditions. We address both a "discrete" case, where the transmitter can transmit only at a fixed power level, and a "continuous" case, where the transmitter can choose any power level out of a bounded interval. For both cases, we propose online power-allocation algorithms with proven worst-case performance bounds. In addition, we establish lower bounds on the worst-case performance of any online algorithm, and show that our proposed algorithms are optimal.

We study the performance of non-cooperative networks in light of three major topology design and control considerations, namely the price of establishing a link, path delay, and path proneness to congestion or interference, the latter being modeled through the "relaying extent" of the nodes. We analyze these considerations and the tradeoffs between them from a game theoretic perspective, where each network element attempts to optimize its individual performance. We show that for all considered cases but one, the existence of a Nash equilibrium point is guaranteed. In addition, we demonstrate that the price of anarchy, i.e., the performance penalty incurred by non-cooperative behavior, may be prohibitively large; yet, we also show that such games usually admit at least one Nash equilibrium that is system-wide optimal, i.e., their price of stability is 1. This finding suggests that a major improvement can be achieved by providing a central ("social") agent with the ability to impose the initial configuration on the system.

Security breaches and attacks are critical problems in today's networking. A key-point is that the security of each host depends not only on the protection strategies it chooses to adopt but also on those chosen by other hosts in the network. The spread of Internet worms and viruses is only one example. This class of problems has two aspects. First, it deals with epidemic processes, and as such calls for the employment of epidemic theory. Second, the distributed and autonomous nature of decision-making in major classes of networks (e.g., P2P, ad- hoc, and most notably the Internet) call for the employment of game theoretical approaches. Accordingly, we propose a unified framework that combines the N-intertwined, SIS epidemic model with a noncooperative game model. We determine the existence of a Nash equilibrium of the respective game and characterize its properties. We show that its quality, in terms of overall network security, largely depends on the underlying topology. We then provide a bound on the level of system inefficiency due to the noncooperative behavior, namely, the "price of anarchy" of the game. We observe that the price of anarchy may be prohibitively high, hence we propose a scheme for steering users towards socially efficient behavior.

Topology control is the task of establishing an efficient underlying graph for ad-hoc networks over which high level routing protocols are implemented. The following design goals are of fundamental importance for wireless topologies: (1) low level of interference; (2) minimum energy consumption; (3) high spatial reuse; (4) connectivity; (5) planarity; (6) sparseness; (7) symmetry; (8) small nodal degree; (9) communication-efficient and localized construction. Previous topology control algorithms have usually been designed to provide good performance guarantees in the worst case. Yet, since design goals often conflict, it is usually impossible to construct a single structure that concurrently addresses a large number of goals efficiently. On the other hand, in this paper we show that a substantially larger number of design goals can concurrently be addressed when "pathological" worst case scenarios are ignored. Accordingly, we focus on average performance and establish a protocol that satisfies all the above design goals. Specifically, we formally prove the efficiency of our protocol with respect to all design goals except for high spatial reuse and small nodal degree, for which this is demonstrated by way of simulations. We note that minimum energy consumption and low level of interference have been the main targets of topology control, and our protocol is proven to offer salient performance guarantees with respect to both.

At present, service providers have several incentives to extend the reach of long-lived MPLS paths across domains. Providers, however, will face a number of trade-offs while choosing the optimal set of MPLS paths to be established. In this paper, we focus on the multi-objective decision problem of maximizing the traffic demands to be covered by long-lived MPLS paths from a source domain S to its major destination domains, while minimizing the monetary costs incurred. The problem is formulated subject to a budget constraint, which assures the minimum expected revenue for the provider in S. A major advantage of the analysis and solution proposed in this paper is that it can be easily generalized, and applied in other settings where constrained problems considering maximum coverage vs. cost are critical.

We present a distributed routing algorithm for finding two disjoint (primary and backup) QoS paths that run across multiple domains. Our work is inspired by the recent interest in establishing communication paths with QoS constrains spanning multiple IP/MPLS domains. In such settings, the routing decisions in each domain are made by the path computation element (PCE). We assume that the PCEs run a joint distributed routing protocol, decoupled from the BGP, which enables them to establish efficient paths across multiple domains. This study makes the following contributions. First, we present an aggregated representation of a multi-domain network that is small enough to minimize the link-state overhead, and, at the same time, is sufficiently accurate, so that the PCEs can find optimal disjoint QoS paths across multiple domains. Second, we present a distributed routing algorithm that uses the proposed representation to find disjoint paths in an efficient manner. Finally, we consider the problem of finding two disjoint paths subject to the export policy limitations, imposed by customer-provider and peer relationships between routing domains. We show that this problem can be efficiently solved by employing the concept of line graphs. To the best of our knowledge, this is the first scheme fully decoupled from BGP that enables to establish disjoint QoS IP/MPLS paths in a multi-domain environment with provable performance guarantees.

Routing traffic so as to maximize the lifetime of a transmission is a major problem in wireless networks. We address a two-way multicast problem, where a root wishes to transmit data to a subset of nodes, as well as receive data from them. In addition, we consider the anycast problem, wherethere is a subset of nodes that wish to communicate with each other. We consider both a per-hop multi-recipients environment, where over each hop, the transmission is received by all nodes within range, and a per-hop single-recipient environment, where over each hop the transmission is received by a single recipient. For both environments, our work consists of two parts. In the first part we focus on system optimization perspectives of the lifetime maximization problem, while in the second part we investigate the game-theoretic perspective of the respective problems.We first note that, for the per-hop multi-recipients environment, an optimal solution can be computed in polynomial time. Nevertheless, for the per-hop single-recipient environment, we observe that computing an optimal solution is NP-hard. Accordingly, we provide a polynomial time algorithm that finds a 2-approximate solution for the case of uniform transmission power levels. For different transmission power levels, we provide an O(log2n) approximation algorithm for the general problem, and an O(log n) approximation algorithm for the special case where the set of terminals equals the set of all nodes, whose size equals n.For each environment, we consider the corresponding noncooperative game scenario, and prove that by following the natural game course users converge to a Nash equilibrium. For the per-hop multi-recipients environment, we show that if the players join the game sequentially, the Nash equilibrium is (networkwide) optimal. For the per-hop single-recipient environment, we show that the price of anarchy is unbounded. On the other hand, we show that for both environments, the price of stability, where the best Nash equilibrium is considered, is 1; hence, optimal (networkwide) performance can be achieved if the initial configuration can be imposed on the players.

We consider routing games where the performance of each user is dictated by the worst (bottleneck) element it employs. We are given a network, finitely many (selfish) users, each associated with a positive flow demand, and a load-dependent performance function for each network element; the social (i.e., system) objective is to optimize the performance of the worst element in the network (i.e., the network bottleneck). Although we show that such "bottleneck" routing games appear in a variety of practical scenarios, they have not been considered yet. Accordingly, we study their properties, considering two routing scenarios, namely when a user can split its traffic over more than one path (splittable bottleneck game) and when it cannot (unsplittable bottleneck game). First, we prove that, for both splittable and unsplittable bottleneck games, there is a (not necessarily unique) Nash equilibrium. Then, we consider the rate of convergence to a Nash equilibrium in each game. Finally, we investigate the efficiency of the Nash equilibria in both games with respect to the social optimum; specifically, while for both games we show that the price of anarchy is unbounded, we identify for each game conditions under which Nash equilibria are socially optimal.

We consider a multicast game with selfish non- cooperative players. There is a special source node and each player is interested in connecting to the source by making a routing decision that minimizes its payment. The mutual influence of the players is determined by a cost sharing mechanism, which in our case evenly splits the cost of an edge among the players using it. We consider two different models: an integral model, where each player connects to the source by choosing a single path, and a fractional model, where a player is allowed to split the flow it receives from the source between several paths. In both models we explore the overhead incurred in network cost due to the selfish behavior of the users, as well as the computational complexity of finding a Nash equilibrium. The existence of a Nash equilibrium for the integral model was previously established by the means of a potential function. We prove that finding a Nash equilibrium that minimizes the potential function is NP-hard. We focus on the price of anarchy of a Nash equilibrium resulting from the best-response dynamics of a game course, where the players join the game sequentially. For a game with in players, we establish an upper bound of O(radicnlog2n) on the price of anarchy, and a lower bound of Omega(log n/log log n). For the fractional model, we prove the existence of a Nash equilibrium via a potential function and give a polynomial time algorithm for computing an equilibrium that minimizes the potential function. Finally, we consider a weighted extension of the multicast game, and prove that in the fractional model, the game always has a Nash equilibrium.

Usual QoS routing algorithms involve the periodic update of network state information in all the network nodes. Based on this knowledge the QoS routing algorithms select the `best' route. It has been shown in the literature that the performance of these QoS routing algorithms strongly depends on the frequency of updating. We propose a new QoS routing mechanism called Prediction-Based Routing based on predicting the availability of links and routes regardless from the network state information. Consequently, update messages are not required, hence reducing signalling overhead and providing a major enhancement in terms of scalability. We show that the PBR is a viable option compared with usual QoS routing algorithms from the point of view of performance, complexity ad signalling overhead.

We consider routing games where the performance of each user is dictated by the worst (bottleneck) element it employs. We are given a network, finitely many (selfish) users, each associated with a positive flow demand, and a load- dependent performance function for each network element; the social (i.e., system) objective is to optimize the performance of the worst element in the network (i.e., the network bottleneck). Although we show that such routing games appear in a variety of practical scenarios, they have not been considered yet. Accordingly, we study their properties, considering two routing scenarios, namely when a user can split its traffic over more than one path (splittable bottleneck game) and when it cannot (unsplittable bottleneck game). First, we prove that, for both splittable and unsplittable bottleneck games, there is a (not necessarily unique) Nash equilibrium. Then, we consider the rate of convergence to a Nash equilibrium in each game. Finally, we investigate the efficiency of the Nash equilibria in both games with respect to the social optimum; specifically, while for both games we show that the price of anarchy is unbounded, we identify for each game conditions under which Nash equilibria are socially optimal.

Peer-to-peer (P2P) networks suffer from the problem of "free-loaders", i.e., users who consume resources without contributing anything in return. In this paper, we tackle this problem taking a game theoretic perspective by modeling the system as a non-cooperative game. We introduce Equi-Cast, a wide-area P2P multicast protocol for large groups of selfish nodes. EquiCast is the first P2P multicast protocol that is formally proven to enforce cooperation in selfish environments. Additionally, we prove that EquiCast incurs a low constant load on each user.

We consider a multicast game with selfish non-cooperative players. There is a special source node and each player is interested in connecting to the source by making a routing decision that minimizes its payment. The mutual influence of the players is determined by a cost sharing mechanism, which in our case evenly splits the cost of an edge among the players using it. We consider two different models: an integral model, where each player connects to the source by choosing a single path, and a fractional model, where a player is allowed to split the flow it receives from the source between several paths. In both models we explore the overhead incurred in network cost due to the selfish behavior of the users, as well as the computational complexity of finding a Nash equilibrium.The existence of a Nash equilibrium for the integral model was previously established by the means of a potential function. We prove that finding a Nash equilibrium that minimizes the potential function is NP-hard. We focus on the price of anarchy of a Nash equilibrium resulting from the best-response dynamics of a game course, where the players join the game sequentially. For a game with n players, we establish an upper bound of O(√n log2n) on the price of anarchy, and a lower bound of Ω(log n/ log log n). For the fractional model, we prove the existence of a Nash equilibrium via a potential function and give a polynomial time algorithm for computing an equilibrium that minimizes the potential function. Finally, we consider a weighted extension of the multicast game, and prove that in the fractional model, the game always has a Nash equilibrium.

We study the problem of optimal packet coding for connections with large delay-bandwidth products. Generally, for a given loss rate, using a higher coding redundancy achieves a higher average throughput, but incurs higher transmission costs (e.g. in terms of energy of a wireless device) and creates a higher load on the network. We define an optimal coding strategy as one that minimizes the expected cost/throughput ratio, for a connection that has a cost per unit time and a cost per transmitted packet. We present an algorithm for computing the optimal strategy and study its properties. We demonstrate that the cost/throughput ratio can be significantly better than with simple retransmission schemes, show that it strongly depends on the decoding buffer size, and obtain several asymptotic bounds on the optimal strategy performance for both unlimited and fixed-size decoding buffers

A major problem in wireless networks is how to route either broadcast, unicast or multicast traffic so as to maximize the lifetime, i.e., the time until the battery of a transmitting node drains out. Focusing on the fundamental single-session problem, our solution approach is based on the employment of multi-topology routing schemes. Such a scheme consists of a set of routing topologies, which are employed sequentially, for some prescribed duration times.First, we consider the standard wireless environment of multiple recipients, which correspond to omnidirectional antennas. For the cases of either single-topology schemes or unicast sessions, we establish optimal solutions of polynomial complexity. For the general (multi-topology) cases of broadcast and multicast, which are NP-hard, we derive a novel heuristic scheme, and demonstrate its efficiency by way of simulations.We then consider an alternative, single-recipient wireless environment, which corresponds to the important case of directional antennas. While the employment of directional antennas is known to posses significant advantages over the traditional omnidirectional transmission, the problem of lifetime maximization under this environment has received only limited attention.We demonstrate that the change from the traditional (multiple-recipients) environment to the single-recipient environment is of major significance in terms of computational complexity and produces an interesting twist of difficulty: namely, for the standard model, the single-topology broadcast problem is computationally solvable and the multi-topology problem is NP-hard, while the opposite holds for the single-recipient model. Finally, we discuss the extension of our results to the case of multiple sessions.

Summary form only given. Broadband integrated services networks are expected to support multiple and diverse applications with various quality of service (QoS) requirements. Accordingly, a major issue in the design of broadband architectures is how to provide the resources in order to meet the requirements of each connection, and, moreover, how to meet this goal in a networkwide efficient manner. QoS routing is, undoubtedly, one of the major building blocks in such architectures. However, QoS routing poses several major algorithmic challenges. One complication is the inherent intractability of many fundamental QoS routing problems. A second challenge is the need to provide scalable solutions, which can cope with the growing sizes of networks. An additional complication lies in the typical uncertainty regarding the precise state of the network. All these become ever more challenging when addressing multicast connections. Moreover, a successful QoS routing scheme should smoothly integrate with other QoS-enabling mechanisms, most notably schedulers. Finally, the practical deployment of QoS routing requires to successfully integrate it within standard routing protocols. These major challenges call for novel algorithmic approaches and solution schemes, which are the subject of this talk. We shall overview some typical problems and solution approaches, focusing on three representative models. The first is a "basic" model, where each network element can offer a certain degree of QoS at a certain "cost". In the second, "extended" model, each network element may offer various degrees of QoS, at different "costs". Finally, in the "coupled" model, the tasks of routing and scheduling are tackled together, hence providing a more precise assessment of the actual consumption of resources. We shall consider the support of bottleneck and additive QoS requirements, both for unicast as well as multicast connections, also in the presence of network failures. We shall focus on solution schemes that provide proven performance guarantees within efficient (polynomial) time complexity for general network topologies. We shall overview several approaches for improving scalability, with a particular focus on precomputation schemes. We shall indicate how this algorithmic framework can address problems of special practical interest, such as the need to cope with state uncertainty

There is a growing interest among service providers to offer new services with Quality of Service (QoS) guarantees that are also resilient to failures. Supporting QoS connections requires the existence of a routing mechanism, that computes the QoS paths, i.e., paths that satisfy QoS constraints (e.g., delay or bandwidth). Resilience to failures, on the other hand, is achieved by providing, for each primary QoS path, a set of alternative QoS paths used upon a failure of either a link or a node. The above objectives, coupled with the need to minimize the global use of network resources, imply that the cost of both the primary path and the restoration topology should be a major consideration of the routing process. We undertake a comprehensive study of problems related to finding suitable restoration topologies for QoS paths. We consider both bottleneck QoS constraints, such as bandwidth, and additive QoS constraints, such as delay and jitter. This is the first study to provide a rigorous solution, with proven guarantees, to the combined problem of computing QoS paths with restoration. It turns out that the widely used approach of disjoint primary and restoration paths is not an optimal strategy. Hence, the proposed algorithms construct a restoration topology , i.e., a set of bridges, each bridge protecting a portion of the primary QoS path. This approach guarantees to find a restoration topology with low cost when one exists.

Supporting quality of service (QoS) in large-scale broadband networks poses major challenges, due to the intrinsic complexity of the corresponding resource allocation problems. An important problem in this context is how to partition QoS requirements along a selected topology (path for unicast and tree for multicast). As networks grow in size, the scalability of the solution becomes increasingly important. This calls for efficient algorithms, whose computational complexity is less dependent on the network size. In addition, recently proposed precomputation-based methods can be employed to facilitate scalability by significantly reducing the time needed for handling incoming requests. We present a novel solution technique to the QoS partition problem(s), based on a "divide-and-conquer" scheme. As opposed to previous solutions, our technique considerably reduces the computational complexity in terms of dependence on network size; moreover, it enables the development of precomputation schemes. Hence, our technique provides a scalable approach to the QoS partition problem, for both unicast and multicast. In addition, our algorithms readily generalize to support QoS routing in typical settings of large-scale networks.

We study the problem of optimal packet coding for connections with large delay-bandwidth products. Generally, for a given loss rate, using a higher coding redundancy achieves a higher average throughput, but also incurs higher transmission costs (e.g. in terms of energy of a wireless device) and creates a higher load on the network. We define an optimal coding strategy as one that minimizes the expected cost/throughput ratio, for a connection that has a cost per unit time and a cost per transmitted packet. We present an algorithm for computing the optimal strategy and study its properties. We demonstrate that the cost/throughput ratio can be significantly better than with the simple retransmission schemes, showing, in particular, that it strongly depends on the decoding buffer size, and obtain several asymptotic bounds on the optimal strategy performance for both unlimited and fixed-size decoding buffers.

Current survivability schemes typically offer two degrees of protection, namely full protection (from a single failure) or no protection at all. Full protection translates into rigid design constraints, i.e. the employment of disjoint paths. We introduce the concept of tunable survivability that bridges the gap between full and no protection. First, we establish several fundamental properties of connections with tunable survivability. With that at hand, we devise efficient polynomial (optimal) connection establishment schemes for both 1:1 and 1+1 protection architectures. Then, we show that the concept of tunable survivability gives rise to a novel hybrid protection architecture, which offers improved performance over the standard 1:1 and 1+1 architectures. Next, we investigate some related QoS extensions. Finally, we demonstrate the advantage of tunable survivability over full survivability. In particular, we show that, by just slightly alleviating the requirement of full survivability, we obtain major improvements in terms of the "feasibility" as well as the "quality" of the solution.

We study the problem of shared path protection in optical networks from the viewpoint of blocking probability minimization. Unlike the worst-case approach common in other studies, which typically deals with one failure at a time and requires recomputation of the protection paths after every failure, our framework assumes a fixed path protection strategy for every connection that does not change in response to failures in other connections, which is more realistic for networks with high failure rates. We study backup-path strategy configurations that minimize the blocking probability and derive various properties. We show that configurations which do not have partial overlaps among connections backup paths are optimal in a rather general sense. We discuss the minmax optimal configuration properties and present an efficient algorithm for finding it in a case of special interest, while showing it to be NP-hard in general. In addition, we discuss the properties of the game resulting if each connection chooses its backup path selfishly; we show it to belong to the class of potential games, well-studied in the game theory literature, and derive several further properties resulting from its specific structure.

Networks are expected to meet a growing volume of requirements imposed by new applications such as multimedia streaming and video conferencing. Two essential requirements are support of quality of service (QoS) and resilience to failures. In order to satisfy these requirements, a common approach is to use two disjoint paths between the source and the destination nodes, the first serving as a primary path and the second as a restoration path. Such approach, referred to as path restoration, has several advantages, the major one being the ability to switch promptly from one path to another in the event of a failure. A major issue in this context is how to identify two paths that satisfy the QoS constraints imposed by network applications. Since network resources, e.g., bandwidth, are allocated along both primary and restoration paths, we need to consider also the overall network performance. Accordingly, in this paper we study the fundamental problem of finding two disjoint paths that satisfy the QoS constraints at minimum cost. We present approximation algorithms with provable performance guarantees for this fundamental network problem.

This work presents a methodology for providing QoS guarantees by considering the coupling between the scheduling mechanism and the routing schemes. Our main focus are rate-based schedulers and stochastic guarantees. We consider several traffic models and obtain for each an appropriate upper bound on the end-to-end delay tail distribution. With that at hand, we derive corresponding routing schemes that exploit the obtained bound. More specifically, we consider traffic with exponentially bounded burstiness (EBB) and stochastic QoS requirements. First, we extend previous results and provide an upper bound on the tail distribution of the end-to-end delay for packetized traffic and links with non-negligible propagation delays. Consequently, we formulate several routing schemes that identify feasible paths under various network optimization criteria. We demonstrate the efficiency of these routing schemes via simulation examples. Then, we consider traffic with (general) stochastic bounded burstiness (SBB). Here, we provide the corresponding upper bound on the end-to-end delay tail distribution for packetized traffic and links with propagation delays. Finally, focusing on the special case of a bounding function that is the sum of exponents, we design appropriate routing schemes.

A method commonly used for packet flow control over connections with long round-trip delays is "sliding windows". In general, for a given loss rate, a larger window size achieves a higher average throughput, but also a higher rate of spurious packet transmissions, rejected by the receiver merely for arriving out-of-order. We analyze the problem of optimal flow control quantitatively, for a connection that has a cost per unit time and a cost for every transmitted packet (these costs can have generic interpretations, not necessarily in terms of money). The optimal strategy is defined as one that minimizes the expected cost/throughput ratio, and is allowed to transmit several copies of a packet within a window. We derive bounds on the performance of the optimal strategy; in particular, we show that the optimal cost/throughput ratio increases merely logarithmically with the time price. We present a method for computing the optimal strategy, and demonstrate that a simple and efficient 'greedy' algorithm is sufficient to find a near-optimal solution.

The problems related to supporting multicast connections with quality of service (QoS) requirements are studied. We investigate the problem of optimal resource allocation in the context of performance dependent costs. In this context each network element can offer several QoS guarantees, each associated with a different cost. This is a natural extension to the commonly used bi-criteria model, where each link is associated with a single delay and a single cost. This framework is simple yet strong enough to model many practical interesting networking problems. The fundamental multicast resource allocation problem under this framework is how to optimally allocate QoS requirements on the links of the multicast tree. One needs to partition the end-to-end QoS requirement along the various paths in a tree. The goal is to satisfy the end-to-end QoS requirement with minimum cost. Previous studies under this framework considered single-source multicast connections, where the end-to-end QoS requirement is specified from the source to all other multicast group members. In this paper we extend these results to the more general, and considerably harder case of multicast sessions, where the end-to-end requirement hold for every path between any two multicast group members. Our aim is to provide rigorous solutions, with proven performance guarantees, by way of algorithmic analysis. The problem under investigation is NP hard for general cost functions, thus we first present a pseudopolynomial exact solution. From this solution we derive two efficient /spl epsi/-approximate solutions. One achieves optimal cost, but may violate the end-to-end delay requirement by a factor of (1 + /spl epsi/), and the other strictly obeys the bounds and achieves a cost within a factor of (1+/spl epsi/) of the optimum. Furthermore, we present improved results for discrete cost functions, and give a simple linear-time exact polynomial solution for a specific, and practically interesting, family of convex cost functions.

Precomputation-based methods have recently been proposed as an instrument to facilitate scalability, improve response time, and reduce computation load on network elements. The key idea is, in effect, to reduce the time needed to handle an event by performing some computation in advance, i.e., prior to the event's arrival. Such computations are performed as background processes, enabling a solution to be provided promptly upon a request, through a simple, fast procedure. We investigate precomputation methods in the context of quality-of-service (QoS) routing. Precomputation is highly desirable for QoS routing schemes due to the high computational complexity of selecting QoS paths, and the need to provide a satisfactory path promptly upon a request. We consider two major settings of QoS routing. The first case is where the QoS constraint is of the "bottleneck" type, e.g., a bandwidth requirement, and network optimization is sought through hop minimization. The second is the more general setting of "additive" QoS constraints (e.g., delay) and general link costs. The paper mainly focuses on the first setting. We show that, by exploiting the typical hierarchical structure of large-scale networks, a substantial improvement can be achieved in terms of computational complexity. We consider networks with topology aggregation. We show that precomputation is a necessary element for any QoS routing scheme and establish a precomputation scheme appropriate for such settings. We consider the case of additive QoS constraints (e.g., delay) and general link costs. As the routing problem becomes NP-hard, we focus on /spl epsiv/-optimal approximations and derive a precomputation scheme that offers a major improvement over the standard approach.

Supporting quality of service (QoS) in large-scale broadband networks poses major challenges, due to the intrinsic complexity of the corresponding resource allocation problems. An important problem in this context is how to partition QoS requirements along a selected topology (path for unicast, tree for multicast). As networks grow in size, the scalability of the solution becomes increasingly important. This requires us to devise efficient algorithms, whose computational complexity is less dependent on the network size. In addition, recently proposed precomputation-based methods can be employed to facilitate scalability by significantly reducing the time needed for handling incoming requests. We present a novel solution technique to the QoS partition problem(s), based on a "divide and conquer" scheme. As opposed to previous solutions, our technique considerably reduces the computational complexity in terms of dependence on network size; moreover, it enables the development of precomputation schemes. Hence, our technique provides a scalable approach to the QoS partition problem, for both unicast and multicast. In addition, our algorithms readily generalize to support QoS routing in typical settings of large-scale networks.

In this paper, we introduce and investigate a "new" path optimization problem that we denote the all hops optimal path (AHOP) problem. The problem involves identifying, for all hop counts, the optimal, i.e., minimum weight, path(s) between a given source and destination(s). The AHOP problem arises naturally in the context of quality-of-service (QoS) routing in networks, where routes (paths) need to be computed that provide services guarantees, e.g., delay or bandwidth, at the minimum possible "cost" (amount of resources required) to the network. Because service guarantees are typically provided through some form of resource allocation on the path (links) computed for a new request, the hop count, which captures the number of links over which resources are allocated, is a commonly used cost measure. As a result, a standard approach for determining the cheapest path available that meets a desired level of service guarantees is to compute a minimum hop shortest (optimal) path. Furthermore, for efficiency purposes, it is desirable to precompute such optimal minimum hop paths for all possible service requests. Providing this information gives rise to solving the AHOP problem. The paper's contributions are to investigate the computational complexity of solving the AHOP problem for two of the most prevalent cost functions (path weights) in networks, namely, additive and bottleneck weights. In particular, we establish that a solution based on the Bellman-Ford algorithm is optimal for additive weights, but show that this does not hold for bottleneck weights for which a lower complexity solution exists.

The notion of timeout (i.e., the maximal time to wait before retrying an action) occurs in many networking contexts. Use of timeouts is encountered especially in large-scale networks, where negative acknowledgments (NACKs) on failures have significantly higher delays than positive acknowledgments (ACKs) and frequently are not employed at all. Selection of a proper timeout involves a tradeoff between waiting too long and loading the network needlessly by waiting too little. The common approach is to set the timeout to a large value, such that, unless the action fails, it is acknowledged within the timeout duration with a high probability. This approach leads to overly long, far from optimal, timeouts. Our quantitative approach has the purpose of computing and studying the optimal timeout strategy. The tradeoff is modeled by introducing a "cost" per unit time (until success) and a "cost" per repeated attempt. The optimal strategy is then defined as one that a selfish user would follow to minimize its expected cost. We discuss various practical interpretations of these costs. We then derive formulas for the optimal timeout values and study some of their fundamental properties. We identify the worthwhile conditions for making parallel attempts from the outset. We also demonstrate a striking property of positive feedback and study the interaction resulting when many users selfishly apply the optimal timeout strategy; we use a noncooperative game model and show that it suffers from an inherent instability problem. Some implications of these results on network design are discussed.

We investigate the problem of optimal resource allocation for end-to-end QoS requirements on unicast paths and multicast trees. Specifically, we consider a framework in which resource allocation is based on local QoS requirements at each network link, and associated with each link is a cost function that increases with the severity of the QoS requirement. Accordingly, the problem that we address is how to partition an end-to-end QoS requirement into local requirements, such that the overall cost is minimized. We establish efficient (polynomial) solutions for both unicast and multicast connections. These results provide the required foundations for the corresponding QoS routing schemes, which identify either paths or trees that lead to minimal overall cost. In addition, we show that our framework provides better tools for coping with other fundamental multicast problems, such as dynamic tree maintenance.

This paper provides an initial look at how support for advance reservations affects the complexity of the path selection process in networks. Advance reservations are likely to become increasingly important as networks and distributed applications become functionally richer and there have been a number of previous works and investigations that explored various related aspects. However, the impact or advance reservations on path selection is a topic that has been left largely untouched. This paper investigates several service models for advance reservations, which range from the traditional basic model of reserving a given amount of bandwidth for some time in the future, to more sophisticated models aimed at increasing the flexibility of services available through advance reservations. The focus is primarily on the issue of computational complexity when supporting advance reservations, and in that context, we derive a number of algorithms and/or intractability results for the various models we consider.

A major algorithmic challenge posed by QoS routing is the need to promptly identify a suitable path upon a connection request, while at the same time ensuring that the selected path is satisfactory, both in terms of the connection's QoS requirements, as well as in terms of the global utilization of network resources. In many practical cases, a precomputation scheme offers a suitable solution to the problem: a background process prepares a database, which enables identification of a suitable path upon each connection request, through a simple, fast, procedure. While much work has been done in terms of path selection algorithms, the precomputation perspective has received little attention. Simplistic adaptations or standard algorithms turn out to be inefficient. Accordingly, we consider the precomputation perspective, focusing on two major settings of QoS routing. The first is the (practically important) special case where the QoS constraint is of the "bottleneck" type, e.g., a bandwidth requirement, and network optimization is sought through hop minimization. For this setting, the standard Bellman-Ford algorithm offers a straightforward precomputation scheme. However, we show that by exploiting the typical hierarchical structure of large-scale networks, one can achieve a substantial improvement in terms of computational complexity. Then, we turn to consider the more general setting of "additive" QoS constraints (e.g., delay) and general link costs. As the routing problem becomes NP-hard, we focus on /spl epsiv/-optimal approximations, and derive a precomputation scheme that offers a major improvement over the standard approach.

Communication networks typically provide a basic best-effort service category, in which resources are shared by concurrent users. As no QoS guarantees are provided, a user will submit to best-effort service only if the expected QoS meets some minimal, user-specific, requirements. This results in an inherent conflict of interest among users, which we capture through a dynamic noncooperative game model and investigate its structure and properties. Specifically, we study the operating points of such systems, i.e., their Nash equilibria. First, we investigate the optimal user strategies, which involve a prediction of the evolving system state, and show that they are of the threshold type. We then establish that a Nash equilibrium point exists and is unique. An algorithmic scheme for computing the Nash equilibrium is provided. In practice, rather than making complex predictions, users typically employ simple decision rules, based on what they learn by experience. Interestingly, it can be shown that the Nash equilibrium of the considered system is a stationary point of such learning schemes. Moreover, we demonstrate that the decisions of users which employ such schemes converge to the Nash equilibrium. Finally, we discuss the implications of the study on network design and management.

QoS routing mechanisms allow users identify paths that can accommodate their performance requirements and reserve the necessary resources. An important problem is how to conduct such resource allocation efficiently, not only from the single-connection, but also from the network point of view. We propose the use of pricing mechanisms as a means to regulate the users decisions in a networkwide efficient manner. Focusing on QoS architectures that employ rate-based schedulers, we formulate a congestion-based pricing scheme. We establish the structure of the corresponding user-optimal response, i.e., a path selection algorithm that satisfies the user's requirements at minimal cost. We show that the underlying noncooperative game among users has a unique equilibrium, for any particular choice of price functions. Then, we establish the existence of incentive compatible price functions, which drive the network into an equilibrium point that coincides with the optimum of a social function. Specifically, these price functions are the derivatives of the social function. We then extend our results to the case in which users can identify only sub-optimal paths, as is often the case with multiobjective path optimization.

We investigate the problem of optimal resource allocation for end to-end QoS requirements on unicast paths and multicast trees. Specifically, we consider a framework in which resource allocation is based on local QoS requirements at each network link, and associated with each link is a cost function that increases with the severity of the QoS requirement. Accordingly, the problem that we address is how to partition an end-to-end QoS requirement into local requirements, such that the overall cost is minimized. We establish efficient (polynomial) solutions for both unicast and multicast connections. These results provide the required foundations for the corresponding QoS routing schemes, which identify either paths or trees that lead to minimal overall cost. In addition, we show that our framework provides better tools for coping with other fundamental multicast problems, such as dynamic tree maintenance.

This paper investigates the problem of routing flows with quality-of-service (QoS) requirements through one or more networks, when the information available for making such routing decisions is inaccurate. Inaccuracy in the information used in computing QoS routes, e.g., network state such as link and node metrics, arises naturally in a number of different environments that are reviewed in the paper. The goal is to determine the impact of such inaccuracy on the ability of the path-selection process to successfully identify paths with adequate available resources. In particular, we focus on devising algorithms capable of selecting path(s) that are most likely to successfully accommodate the desired QoS, in the presence of uncertain network state information for the purpose of the analysis, we assume that this uncertainty is expressed through probabilistic models, and we briefly discuss sample cases that can give rise to such models. We establish that the impact of uncertainty is minimal for flows with only bandwidth requirements, but that it makes path selection intractable when end-to-end delay requirements are considered. For this latter case, we provide efficient solutions for special cases of interest and develop useful heuristics.

In noncooperative networks, resources are shared among selfish users, which optimize their individual performance measure. Traditional design methods tend to perform poorly in such networks, as they do not take into account the inherent noncooperative nature of the network users. Such networks require specialized design techniques in order to achieve efficient utilization of resources. We consider the generic and practically important class of atomic resource sharing networks, in which traffic bifurcation is not implemented, hence each user allocates its whole traffic to one of the network resources. We investigate topologies of parallel resources within a game-theoretic framework and establish the foundations of a design and management methodology that enables operation of such networks efficiently, despite both the lack of cooperation among users and the restrictions imposed by atomic resource sharing. We study various problems pertaining to capacity allocation, pricing, and admission control, and show that their solutions are substantially different from those corresponding to traditional networks.

We consider routing schemes for connections with end-to-end delay requirements, and investigate several fundamental problems. First, we focus on networks which employ rate-based schedulers and, hence, map delay guarantees into nodal rate guarantees, as done with the guaranteed service class proposed for the Internet. We consider first the basic problem of identifying a feasible route for the connection, for which a straightforward yet computationally costly solution exists. Accordingly, we establish several approximation schemes that offer substantially lower computational complexity. We then consider the more general problem of optimizing the route choice in terms of balancing loads and accommodating multiple connections, for which we formulate and validate several optimal algorithms. We discuss the implementation of such schemes in the context of link-state and distance-vector protocols. Next, we consider the fundamental problem of constrained path optimization. This problem, typical of quality of service routing, is NP-hard. While standard approximation methods exist, their complexity may often be prohibitive in terms of scalability. Such approximations do not make use of the particular properties of large-scale networks, such as the face that the path selection process is typically presented with a hierarchical, aggregated topology. By exploiting the structure of such topologies, we obtain an /spl epsiv/-optimal algorithm for the constrained shortest-path problem, which offers a substantial improvement in terms of scalability.

Modern communication networks evolve towards integration of guaranteed-performance and best-effort service types. The co-existence of these two service types offers substantial benefits, such as resource sharing between service classes, and the ability of the user to select an appropriate service class according to its individual requirements and preferences. Notwithstanding, such interaction potentially complicates the system behavior, and gives rise to subtle optimization questions, which need to be explored and understood in order to allow efficient network operation. In this paper we address some essential performance and flow control issues associated with such service interactions. We propose a fluid model for session flow, which captures the two interaction mechanisms of resource sharing. In particular, our model incorporates the possibility of session migration, where sessions may shift from best effort to guaranteed performance service due to congestion experienced in the former. Within this model, we analyze the system performance and characterize its steady state behavior. We further show that under certain conditions the system exhibits bistable behavior, where some transient congestion may stir the system from a stable and efficient operating point to an inefficient and congested one, which might persist indefinitely. For the latter case, we propose a call admission control scheme which prevents the system from getting trapped in a congested-type equilibrium, while not interfering with normal system operation.

This article considers the problem of routing connections with QoS requirements across networks, when the information available for making routing decisions is inaccurate. This uncertainty about the actual state of a network component arises naturally in a number of different environments, which are reviewed in the paper. The goal of the route selection process is then to identify a path that is most likely to satisfy the QoS requirements. For end to end delay guarantees, this problem is intractable. However we show that by decomposing the end-to-end constraint into local delay constraints, efficient and tractable solutions can be established. We first consider the simpler problem of decomposing the end-to-end constraint into local constraints, for a given path. We show that, for general distributions, this problem is also intractable. Nonetheless, by defining a certain class of probability distributions, which posses a certain convexity property, and restricting ourselves to that class, we are able to establish efficient and exact solutions. Moreover, we show that typical distributions would belong to that class. We then consider the general problem, of combined path optimization and delay decomposition. We present an efficient solution scheme for the above class of probability distributions. Our solution is similar to that of the restricted shortest-path problem, which renders itself to near-optimal approximations of polynomial complexity. We also show that yet simpler solutions exist in the special case of uniform distributions.

We consider routing schemes for connections with end to end delay requirements, and investigate several fundamental problems. First, we focus on networks which employ rate-based schedulers and hence map delay guarantees into nodal rate guarantees, as done with the guaranteed service class proposed for the Internet. We consider first the basic problem of identifying a feasible route for the connection, for which a straightforward, yet computationally costly solution exists. Accordingly, we establish several /spl epsiv/-optimal solutions that offer substantially lower computational complexity. We then consider the more general problem of optimizing the route choice in terms of balancing loads and accommodating multiple connections, for which we formulate and validate several optimal algorithms. We discuss the implementation of such schemes in the context of link-state and distance-vector protocols. Next, we consider the fundamental problem of constrained path optimization. This problem, typical of QoS routing, is NP-hard. While standard approximation methods exist, their complexity may often be prohibitive in terms of scalability. Such approximations do not make use of the particular properties of large-scale networks, such as the fact that the path selection process is typically presented with a hierarchical, aggregated topology. By exploiting the structure of such topologies, we obtain an /spl epsiv/-optimal algorithm for the constrained shortest path problem, which offers a substantial improvement in terms of scalability.

We consider the problem of routing connections with quality of service (QoS) requirements across networks when the information available for making routing decisions is inaccurate. Such uncertainty about the actual state of a network component arises naturally in a number of different environments. The goal of the route selection process is then to identify a path that is most likely to satisfy the QoS requirements. For end-to-end delay guarantees, this problem is intractable. However, we show that by decomposing the end-to-end constraint into local delay constraints, efficient and tractable solutions can be established. Moreover, we argue that such decomposition better reflects the interoperability between the routing and reservation phases. We first consider the simpler problem of decomposing the end-to-end constraint into local constraints for a given path. We show that, for general distributions, this problem is also intractable. Nonetheless, by defining a certain class of probability distributions, which includes typical distributions, and restricting ourselves to that class, we are able to establish efficient and exact solutions. We then consider the general problem of combined path optimization and delay decomposition and present efficient solutions. Our findings are applicable also to a broader problem of finding a path that meets QoS requirements at minimal cost, where the cost of each link is some general increasing function of the QoS requirements from the link.

We investigate the problem of routing connections with QoS requirements across one or more networks, when the information available for making routing decisions is inaccurate and expressed in some probabilistic manner. This uncertainty about the actual state of a node or network arises naturally in a number of different environments, that are reviewed in the paper. The main focus is to determine the impact of such inaccuracies on the path selection process, whose goal is then to identify the path that is most likely to satisfy the QoS requirements.

In noncooperative networks, resources are shared among selfish users, which optimize their individual performance measure. We consider the generic and practically important case of atomic resource sharing, in which traffic bifurcation is not implemented, hence each user allocates its whole traffic to one of the network resources. We analyze topologies of parallel resources within a game-theoretic framework and establish several fundamental properties. We prove the existence of and convergence to a Nash equilibrium. For a broad class of residual capacity performance functions, an upper bound on the number of iterations till convergence is derived. An algorithm is presented for testing the uniqueness of the equilibrium. Sufficient conditions for achieving a feasible equilibrium are obtained. We consider extensions to general network topologies. In particular, we show that, for a class of throughput-oriented cost functions, existence of and convergence to a Nash equilibrium is guaranteed in all topologies. With these structural results at hand, we establish the foundations of a design and management methodology, that enables one to operate such networks efficiently, in spite of the lack of cooperation among users and the restrictions imposed by atomic resource sharing.

We consider a communication network that offers multi-class services to multiple types of traffic. Users choose service classes so as to optimize their own performance. The network associates with each traffic type a nominal service class. Optimal prices should provide incentives for the users to assign each traffic type to its nominal service class. We establish necessary and sufficient conditions for the existence of optimal prices and provide an algorithm for their computation. We indicate that optimal prices can tolerate fluctuations in the various parameters. We then devise a distributed algorithm, with which the network can compute optimal prices even when it does not have sufficient knowledge on the traffic characteristics. Next, we consider an extended model which explicitly includes congestion effects. A key factor which emerges here is the amount of traffic at the disposal of each user. We consider the typical cases of individual, social and type optimization, for which we generalize our results.

The packet fragmentation problem in computer networks is that of breaking a packet into smaller pieces (fragments) due to packet-size limitations along the packet's route. This is a typical internetworking problem. We show that the commonly used simplistic approach whereby the routing and fragmentation functions operate completely independently is far from being efficient and has adverse effects on network performance. This paper deals with the combined fragmentation-and-routing problem. We discuss several possible fragmentation machines and indicate their equivalence. This enables the formulation of a comprehensive yet tractable flows model, whose performance measure is total network delay. An analysis of this model leads to necessary and sufficient optimality conditions for the fragmentation-and-routing problem. The optimality conditions serve as a base line for devising several optimal algorithms, both centralized and distributed. To deal with minimum first derivative length algorithms, we generalize the concept of minimum first derivative paths in order to accommodate them into our environment. Several special cases of practical interest are discussed. We show how the problem size and the running time of the algorithms are considerably shortened in networks in which packet sizes come in a limited number of sizes. We also show how our approach can accommodate performance measures other than total delay. The case of networks with virtual circuits is also discussed. © 1997 John Wiley & Sons, Inc.

In noncooperative networks users make control decisions that optimize their individual performance objectives. Nash equilibria characterize the operating points of such networks. Nash equilibria are generically inefficient and exhibit suboptimal network performance. Focusing on routing, a methodology is devised for overcoming this deficiency, through the intervention of the network manager. The manager controls part of the network flow, is aware of the noncooperative behavior of the users and performs its routing aiming at improving the overall system performance. The existence of maximally efficient strategies for the manager, i.e., strategies that drive the system into the global network optimum, is investigated. A maximally efficient strategy of the manager not only optimizes the overall performance of the network, but also induces an operating point that is efficient with respect to the performance of the individual users (Pareto efficiency). Necessary and sufficient conditions for the existence of a maximally efficient strategy are derived, and it is shown that they are met in many cases of practical interest. The maximally efficient strategy is shown to be unique and it is specified explicitly.

We consider a multiuser network that is shared by noncooperative users. Each user sets up virtual paths that optimize its own selfish performance measure. This measure accounts for the guaranteed call level quality of service, as well as for the cost incurred for reserving the resource. The interaction among the user strategies is formalized as a noncooperative game. We show that the game has a unique Nash equilibrium and that it possesses a certain fairness property. We investigate the dynamics of this game and prove convergence to the Nash equilibrium of both a Gauss-Seidel scheme and a Jacobi scheme. We extend our study to various general network topologies. Finally, the formal results and some extensions thereof are tested by emulating the schemes on an experimental network.

Traditional computer networks were typically designed with system-wide optimization in mind. In noncooperative networks users make control decisions that optimize their individual performance objectives. Nash equilibria characterize the operating points of such networks. Nash equilibria exhibit, in general, suboptimal network performance. Focusing on routing, a methodology is devised for overcoming this deficiency, through the intervention of the network manager. The manager controls part of the network flow, is aware of the noncooperative behavior of the users and performs its routing aiming at improving the overall system performance. The existence of maximally efficient strategies for the manager, i.e., strategies that drive the system into the global network optimum, is investigated. Necessary and sufficient conditions for the existence of a maximally efficient strategy are derived. The maximally efficient strategy are shown to be unique and it is specified explicitly.

We propose a new policy for virtual path bandwidth allocation in broadband networks. Based on a threshold scheme, our policy handles the inherent tradeoff between bandwidth utilization and processing costs. In each virtual path controller the thresholds are chosen so as to keep bandwidth utilization high, while obtaining a low rate of processing requests. Two novel ideas are used in our threshold scheme: adaptivity, which results in a better prediction of future bandwidth requirements; and hysteresis, which prevents excessive processing of requests due to oscillations around thresholds. We tested the performance of our new bandwidth control scheme, and compared it with previously suggested schemes. The performance measures were the expected amount of unused bandwidth, the average signaling load and the blocking probability. Performance has been evaluated through numerical computations as well as by simulations. Our analysis is based on a time segmentation technique which allows us to reduce a Markov chain with NM states into M Markov chains with N states and a one-dimensional chain with M states. Our results show that our policy significantly improves upon previously suggested approaches.

This paper is concerned with on-line storage allocation to processes in a dynamic environment. This problem has been extensively studied in the past. We provide a new, tighter bound for the competitive ratio of the well-known First Fit algorithm. This bound is obtained by considering a new parameter, namely the maximum number of concurrent active processes. We observe that this bound is also a lower bound on the competitive ratio of any deterministic on-line algorithm. Our second contribution is an on-line allocation algorithm that uses coloring techniques. We show that the competitive ratio of this algorithm is the same as that of First Fit. Furthermore, we indicate that this algorithm may be advantageous in certain applications. Our third contribution is to analyze the performance of randomized algorithms for this problem. We obtain lower bounds on the competitive ratio that are close to the best deterministic upper bounds.

Considers a multi-user network that is shared by noncooperative users. Each user sets up virtual paths that optimize its own, selfish, performance measure. This measure accounts for both the guaranteed call level quality of service, as well as for the cost incurred for reserving the resource. The interaction between the user strategies is formalized as a game. The authors show that this game has a unique Nash equilibrium, and that it possesses a certain fairness property. They investigate the dynamics of this game, and prove convergence to the Nash equilibrium of both a Gauss-Seidel scheme and a Jacobi scheme. They extend their study to various general network topologies.

In noncooperative networks users make control decisions that optimize their individual performance measure. Focusing on routing, two methodologies for architecting noncooperative networks are devised, that improve the overall network performance. These methodologies are motivated by problem settings arising in the provisioning and the run time phases of the network. For either phase, Nash equilibria characterize the operating point of the network. The goal in the provisioning phase is to allocate link capacities that lead to systemwide efficient Nash equilibria. The solution of such design problems is, in general, counterintuitive, since adding link capacity might lead to degradation of user performance. For systems of parallel links, it is shown that such paradoxes cannot occur and that the optimal solution coincides with the solution in the single-user case. Extensions to general network topologies are derived. During the run time phase, a manager controls the routing of part of the network flow. The manager is aware of the noncooperative behavior of the users and makes its routing decisions based on this information while aiming at improving the overall system performance. We obtain necessary and sufficient conditions for enforcing an equilibrium that coincides with the global network optimum, and indicate that these conditions are met in many cases of interest.>

The combined fragmentation-and-routing problem is addressed. Several possible fragmentation machines are discussed, and their equivalence is indicated. This allows the formulation of a comprehensive yet tractable flow model, whose performance measure is total delay. An analysis of this model leads to necessary and sufficient optimality conditions for the fragmentation-and-routing problem. The optimality conditions serve as a baseline for devising several optimal algorithms, both centralized and distributed. In order to deal with minimum first derivative length algorithms, the concept of minimum first derivative paths is generalized in order to accommodate them in the environment used. Several special cases of practical interest are discussed. It is shown the problem size and the running time of the algorithms are considerably shortened in networks in which packet sizes come in a limited number of sizes. The approach can accommodate performance measures other than total delay.>

A communication network shared by several selfish users is considered. Each user seeks to optimize its own performance by controlling the routing of its given flow demand, giving rise to a noncooperative game. The Nash equilibrium of such systems is investigated. For a two-node multiple-link system, the uniqueness of the Nash equilibrium is proved under reasonable convexity conditions. It is shown that this Nash equilibrium point possesses interesting monotonicity properties. For general networks, the uniqueness of the Nash equilibrium is established under various assumptions.>

The authors consider the problem of traveling with least expected delay in networks whose link delays change probabilistically according to Markov chains. This is a typical routing problem in dynamic computer communication networks. Several optimization problems, posed on infinite and finite horizons, are formulated, and they are considered with and without using memory in the decision-making process. It is proved that all these problems are, in general, intractable. However, for networks with nodal stochastic delays, a simple polynomial optimal solution is presented. This is typical of high-speed networks, in which the dominant delays are incurred by the nodes. For more general networks, a tractable in -optimal solution is presented.>

The authors consider a communication network shared by several selfish users. Each user seeks to optimize its own performance by controlling the routing of its given flow demand, giving rise to a noncooperative game. They investigate the Nash equilibrium of such systems. For a two-node multiple links system, uniqueness of the Nash equilibrium is proven under reasonable convexity conditions. It is shown that this Nash equilibrium point possesses interesting monotonicity properties. For general networks, these convexity conditions are not sufficient for guaranteeing uniqueness, and a counterexample is presented. Nonetheless, uniqueness of the Nash equilibrium for general topologies is established under various assumptions.>

The authors consider the problem of traveling with least expected delay in networks whose link delays change probabilistically according to Markov chains. This is a typical routing problem in dynamic computer communication networks. They formulate several optimization problems, posed on infinite and finite horizons, and consider them with and without using memory in the decision making process. It is proved that all these problems are, in general, intractable. However, for networks with nodal stochastic delays, a simple polynomial optimal solution is presented. This is typical of high-speed networks, in which the dominant delays are incurred by the nodes. For more general networks, a tractable epsilon -optimal solution is presented. The performance of a regular shortest-path algorithm in such an environment is considered.>

Abstract We investigate the minimum weight path problem in networks whose link weights and link delays are both functions of time. We demonstrate that, in general, there exist cases in which no finite path is optimal leading us to define an infinite path (naturally, containing loops) in such a way that the minimum weight problem always has a solution. We also characterize the structure of an infinite optimal path. In many practical cases, finite optimal paths do exist. We formulate a criterion that guarantees the existence of a finite optimal path and develop an algorithm to find such a path. Some special cases, e.g., optimal loopless paths, are also discussed.

In this paper the shortest-path problem in networks in which the delay (or weight) of the edges changes with time according to arbitrary functions is considered. Algorithms for finding the shortest path and minimum delay under various waiting constraints are presented and the properties of the derived path are investigated. It is shown that if departure time from the source node is unrestricted, then a shortest path can be found that is simple and achieves a delay as short as the most unrestricted path. In the case of restricted transit, it is shown that there exist cases in which the minimum delay is finite, but the path that achieves it is infinite.

A single-facility dynamic-network location problem with a continuous (rather than discrete) time domain is considered. It is assumed that the network state changes constantly and thus at each moment a different point may be the best choice for facility location. The cost of switching the facility from one node to another is taken into account because this switching consumes resources (although switching does not necessarily involve physical relocation, the cost results from the need to relocate the function). These costs are assumed to be time-dependent.>

The authors consider the shortest-path problem in networks in which the length (or weight) of the edges change with time according to arbitrary functions. They present algorithms for finding the shortest-path and minimum-delay under various waiting constraints and investigate the quality of the derived path. They also show that if departure time from the source node is unrestricted and delay functions are continuous then a shortest path can be found that is simple and achieves a delay as short as the most unrestricted strategy. The optimal waiting time for such cases is also computed. In more restricted transit, it is shown that there exist cases where the minimum delay is finite yet the path that achieves it is infinite.>

Multihoming in networks, i.e. attaching a subscriber to more than a single access point in the network, is a mechanism used to improve performance. The authors take the topological design view and address the problem of finding optimal multihoming configurations for several topological design criteria. They analyze the problem and demonstrate that except for dual homing, multihoming is algorithmically complex. Optimal algorithms based on maximum matching in graphs and 0-1 integer programming are given for all cases.>

Packet duplication is discussed as a means of increasing network reliability in an environment where packet loss exists. Several methods of routing the duplicates are presented, one of which-the st-numbering-is shown to have the combined advantage of using disjoint paths and more even utilization of network resources. An additional mechanism, deliberate packet elimination, is introduced as a means of controlling congestion that may result, in part, from the duplication. A comprehensive model is defined encompassing the process of packet duplication together with both forms of packet elimination. Within this model, a cost function based on average packet delay is defined. A quasi-static distributed algorithm is developed that is optimal, deadlock free, and loop free. Extension of the model to include packet retransmission is considered.>