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126
A tutorial on crosslayer optimization in wireless networks
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2006
"... This tutorial paper overviews recent developments in optimization based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channelaware) scheduling for cellular (singlehop) networks, where easily implementable my ..."
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Cited by 248 (29 self)
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This tutorial paper overviews recent developments in optimization based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channelaware) scheduling for cellular (singlehop) networks, where easily implementable myopic policies are shown to optimize system performance. We then describe key lessons learned and the main obstacles in extending the work to general resource allocation problems for multihop wireless networks. Towards this end, we show that a cleanslate optimization based approach to the multihop resource allocation problem naturally results in a “loosely coupled” crosslayer solution. That is, the algorithms obtained map to different layers (transport, network, and MAC/PHY) of the protocol stack are coupled through a limited amount of information being passed back and forth. It turns out that the optimal scheduling component at the MAC layer is very complex and thus needs simpler (potentially imperfect) distributed solutions. We demonstrate how to use imperfect scheduling in the crosslayer framework and describe recently developed distributed algorithms along these lines. We conclude by describing a set of open research problems.
Lowcomplexity distributed scheduling algorithms for wireless networks
 IEEE/ACM Trans. on Netw
"... Abstract — We consider the problem of distributed scheduling in wireless networks. We present two different algorithms whose performance is arbitrarily close to that of maximal schedules, but which require low complexity due to the fact that they do not necessarily attempt to find maximal schedules. ..."
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Cited by 81 (6 self)
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Abstract — We consider the problem of distributed scheduling in wireless networks. We present two different algorithms whose performance is arbitrarily close to that of maximal schedules, but which require low complexity due to the fact that they do not necessarily attempt to find maximal schedules. The first algorithm requires each link to collect local queuelength information in its neighborhood, and its complexity is independent of the size and topology of the network. The second algorithm is presented for the nodeexclusive interference model, does not require nodes to collect queuelength information even in their local neighborhoods, and its complexity depends only on the maximum node degree in the network. I.
On Combining ShortestPath and BackPressure Routing Over Multihop Wireless Networks
, 2008
"... Abstract—Backpressure based algorithms based on the algorithm by Tassiulas and Ephremides have recently received much attention for jointly routing and scheduling over multihop wireless networks. However a significant weakness of this approach has been in routing, because the traditional backpress ..."
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Cited by 65 (5 self)
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Abstract—Backpressure based algorithms based on the algorithm by Tassiulas and Ephremides have recently received much attention for jointly routing and scheduling over multihop wireless networks. However a significant weakness of this approach has been in routing, because the traditional backpressure algorithm explores and exploits all feasible paths between each source and destination. While this extensive exploration is essential in order to maintain stability when the network is heavily loaded, under light or moderate loads, packets may be sent over unnecessarily long routes and the algorithm could be very inefficient in terms of endtoend delay and routing convergence times. This paper proposes new routing/scheduling backpressure algorithms that not only guarantees network stability (throughput optimality), but also adaptively selects a set of optimal routes based on shortestpath information in order to minimize average pathlengths between each source and destination pair. Our results indicate that under the traditional backpressure algorithm, the endtoend packet delay first decreases and then increases as a function of the network load (arrival rate). This surprising lowload behavior is explained due to the fact that the traditional backpressure algorithm exploits all paths (including very long ones) even when the traffic load is light. On the otherhand, the proposed algorithm adaptively selects a set of routes according to the traffic load so that long paths are used only when necessary, thus resulting in much smaller endtoend packet delays as compared to the traditional backpressure algorithm. I.
Alternative Distributed Algorithms for Network Utility Maximization: Framework and Applications
 IEEE Transactions on Automatic Control
, 2007
"... Abstract—Network utility maximization (NUM) problem formulations provide an important approach to conduct network resource allocation and to view layering as optimization decomposition. In the existing literature, distributed implementations are typically achieved by means of the socalled dual deco ..."
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Cited by 59 (7 self)
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Abstract—Network utility maximization (NUM) problem formulations provide an important approach to conduct network resource allocation and to view layering as optimization decomposition. In the existing literature, distributed implementations are typically achieved by means of the socalled dual decomposition technique. However, the span of decomposition possibilities includes many other elements that, thus far, have not been fully exploited, such as the use of the primal decomposition technique, the versatile introduction of auxiliary variables, and the potential of multilevel decompositions. This paper presents a systematic framework to exploit alternative decomposition structures as a way to obtain different distributed algorithms, each with a different tradeoff among convergence speed, message passing amount and asymmetry, and distributed computation architecture. Several specific applications are considered to illustrate the proposed framework, including resourceconstrained and directcontrol rate allocation, and rate allocation among QoS classes with multipath routing. For each of these applications, the associated generalized NUM formulation is first presented, followed by the development of novel alternative decompositions and numerical experiments on the resulting new distributed algorithms. A systematic enumeration and comparison of alternative vertical decompositions in the future will help complete a mathematical theory of network architectures. Index Terms—Congestion control, distributed algorithm, mathematical programming/optimization, network control by pricing, network utility maximization (NUM), rate control, resource allocation.
Incremental stochastic subgradient algorithms for convex optimization
 SIAM J. OPTIM
, 2008
"... In this paper we study the effect of stochastic errors on two constrained incremental subgradient algorithms. We view the incremental subgradient algorithms as decentralized network optimization algorithms as applied to minimize a sum of functions, when each component function is known only to a ..."
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Cited by 49 (7 self)
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In this paper we study the effect of stochastic errors on two constrained incremental subgradient algorithms. We view the incremental subgradient algorithms as decentralized network optimization algorithms as applied to minimize a sum of functions, when each component function is known only to a particular agent of a distributed network. We first study the standard cyclic incremental subgradient algorithm in which the agents form a ring structure and pass the iterate in a cycle. We consider the method with stochastic errors in the subgradient evaluations and provide sufficient conditions on the moments of the stochastic errors that guarantee almost sure convergence when a diminishing stepsize is used. We also obtain almost sure bounds on the algorithm’s performance when a constant stepsize is used. We then consider the Markov randomized incremental subgradient method, which is a noncyclic version of the incremental algorithm where the sequence of computing agents is modeled as a time nonhomogeneous Markov chain. Such a model is appropriate for mobile networks, as the network topology changes across time in these networks. We establish the convergence results and error bounds for the Markov randomized method in the presence of stochastic errors for diminishing and constant stepsizes, respectively.
Horizon: Balancing tcp over multiple paths in wireless mesh network
 In MobiCom
, 2008
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Optimal Scheduling for Fair Resource Allocation in Ad Hoc Networks with Elastic and Inelastic Traffic
, 907
"... Abstract—This paper studies the problem of congestion control and scheduling in ad hoc wireless networks that have to support a mixture of besteffort and realtime traffic. Optimization and stochastic network theory have been successful in designing architectures for fair resource allocation to mee ..."
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Cited by 33 (4 self)
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Abstract—This paper studies the problem of congestion control and scheduling in ad hoc wireless networks that have to support a mixture of besteffort and realtime traffic. Optimization and stochastic network theory have been successful in designing architectures for fair resource allocation to meet longterm throughput demands. However, to the best of our knowledge, strict packet delay deadlines were not considered in this framework previously. In this paper, we propose a model for incorporating the quality of service (QoS) requirements of packets with deadlines in the optimization framework. The solution to the problem results in a joint congestion control and scheduling algorithm which fairly allocates resources to meet the fairness objectives of both elastic and inelastic flows, and perpacket delay requirements of inelastic flows. I.
Impact of stochastic noisy feedback on distributed network utility maximization
 in INFOCOM 2007
, 2007
"... Abstract — The implementation of distributed network utility maximization (NUM) algorithms hinges heavily on information feedback through message passing among network elements. In practical systems the feedback is often obtained using errorprone measurement mechanisms and suffers from random errors ..."
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Cited by 30 (4 self)
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Abstract — The implementation of distributed network utility maximization (NUM) algorithms hinges heavily on information feedback through message passing among network elements. In practical systems the feedback is often obtained using errorprone measurement mechanisms and suffers from random errors. In this paper, we investigate the impact of noisy feedback on distributed NUM. We first study the distributed NUM algorithms based on the Lagrangian dual method, and focus on the primaldual (PD) algorithm, which is a single timescale algorithm in the sense that the primal and dual parameters are updated simultaneously. Assuming strong duality, we study both cases when the stochastic gradients are unbiased or biased, and develop a general theory on the stochastic stability of the PD algorithms in the presence of noisy feedback. When the gradient estimators are unbiased,
Fast algorithms and performance bounds for sum rate maximization in wireless networks
 in Proceedings of IEEE INFOCOM
, 2009
"... Abstract — Sum rate maximization by power control is an important, challenging, and extensively studied problem in wireless networks. It is a nonconvex optimization problem and achieves a rate region that is in general nonconvex. We derive approximation ratios to the sum rate objective by studying t ..."
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Cited by 28 (10 self)
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Abstract — Sum rate maximization by power control is an important, challenging, and extensively studied problem in wireless networks. It is a nonconvex optimization problem and achieves a rate region that is in general nonconvex. We derive approximation ratios to the sum rate objective by studying the solutions to two related problems, sum rate maximization using an SIR approximation and maxmin weighted SIR optimization. We also show that these two problems can be solved very efficiently, using much faster algorithms than the existing ones in the literature. Furthermore, using a new parameterization of the sum rate maximization problem, we obtain a characterization of the power controlled rate region and its convexity property in various asymptotic regimes. Engineering implications are discussed for IEEE 802.11 networks. Index Terms — Duality, Distributed algorithm, Power control, Weighted sum rate maximization, Nonnegative matrices and applications,
Maximizing Utility via Random Access Without Message Passing
, 2008
"... It has been an intensively soughtafter goal to achieve high throughput and fairness in wireless scheduling through simple and distributed algorithms. Many recent papers on the topic have relied on various types of message passing among the nodes. The following question remains open: can scheduling ..."
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Cited by 27 (4 self)
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It has been an intensively soughtafter goal to achieve high throughput and fairness in wireless scheduling through simple and distributed algorithms. Many recent papers on the topic have relied on various types of message passing among the nodes. The following question remains open: can scheduling without any message passing guarantee throughputoptimality and fairness? Over the last year, it has been suggested in three papers [1]–[3] that random access without message passing may be designed and proved to be optimal in terms of throughput and utility. In this paper, we first extend the algorithm in [2] and provide a rigorous proof of utilityoptimality for random access without message passing for Poisson clock model. Then we turn to the more difficult discrete contention and backoff model with collisions, study its optimality properties, and control a tradeoff between longterm efficiency and shortterm fairness that emerges in this model.