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19
Network Adiabatic Theorem: An Efficient Randomized Protocol for Contention Resolution
"... The popularity of Aloha(like) algorithms for resolution of contention between multiple entities accessing common resources is due to their extreme simplicity and distributed nature. Example applications of such algorithms include Ethernet and recently emerging wireless multiaccess networks. Despit ..."
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Cited by 77 (9 self)
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The popularity of Aloha(like) algorithms for resolution of contention between multiple entities accessing common resources is due to their extreme simplicity and distributed nature. Example applications of such algorithms include Ethernet and recently emerging wireless multiaccess networks. Despite a long and exciting history of more than four decades, the question of designing an algorithm that is essentially as simple and distributed as Aloha while being efficient has remained unresolved. In this paper, we resolve this question successfully for a network of queues where contention is modeled through independentset constraints over the network graph. The work by Tassiulas and Ephremides (1992) suggests that an algorithm that schedules queues so that the summation of “weight ” of scheduled queues is maximized, subject to constraints, is efficient. However, implementing such an algorithm using Alohalike mechanism has remained a mystery. We design such an algorithm building upon a MetropolisHastings sampling mechanism along with selection of“weight” as an appropriate function of the queuesize. The key ingredient in establishing the efficiency of the algorithm is a novel adiabaticlike theorem for the underlying queueing network, which may be of general interest in the context of dynamical systems.
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 30 (11 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,
Crosslayer Optimization for Wireless Networks with Deterministic Channel Models
"... Abstract—Existing work on crosslayer optimization for wireless networks adopts simple physicallayer models, i.e., treating interference as noise. In this paper, we adopt a deterministic channel model proposed in [11, 12], a simple abstraction of the physical layer that effectively captures the eff ..."
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Cited by 8 (4 self)
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Abstract—Existing work on crosslayer optimization for wireless networks adopts simple physicallayer models, i.e., treating interference as noise. In this paper, we adopt a deterministic channel model proposed in [11, 12], a simple abstraction of the physical layer that effectively captures the effect of channel strength, broadcast and superposition in wireless channels. Within the Network Utility Maximization (NUM) framework, we study the crosslayer optimization for wireless networks based on this deterministic channel model. First, we extend the wellapplied conflict graph model to capture the flow interactions over the deterministic channels and characterize the feasible rate region. Then we study distributed algorithms for general wireless multihop networks. The convergence of algorithms is proved by Lyapunov stability theorem and stochastic approximation method. Further, we show the convergence to the bounded neighborhood of optimal solutions with probability one under constant steps and constant update intervals. Our numerical evaluation validates the analytical results. I.
On the limitations of randomization for queuelengthbased scheduling in wireless networks
, 2010
"... Abstract—Randomization is a powerful and pervasive strategy for developing efficient and practical transmission scheduling algorithms in interferencelimited wireless networks. Yet, despite the presence of a variety of earlier works on the design and analysis of particular randomized schedulers, th ..."
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Cited by 6 (6 self)
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Abstract—Randomization is a powerful and pervasive strategy for developing efficient and practical transmission scheduling algorithms in interferencelimited wireless networks. Yet, despite the presence of a variety of earlier works on the design and analysis of particular randomized schedulers, there does not exist an extensive study of the limitations of randomization on the efficient scheduling in wireless networks. In this work, we aim to fill this gap by proposing a common modeling framework and three functional forms of randomized schedulers that utilize queuelength information to probabilistically schedule nonconflicting transmissions. This framework not only models many existing schedulers operating under a timescale separation assumption as special cases, but it also contains a much wider class of potential schedulers that have not been analyzed. Our main results are the identification of necessary and sufficient conditions on the network topology and on the functional forms used in the randomization for throughputoptimality. Our analysis reveals an exponential and a subexponential class of functions that exhibit differences in the throughputoptimality. Also, we observe the significance of the network’s scheduling diversity for throughputoptimality as measured by the number of maximal schedules each link belongs to. We further validate our theoretical results through numerical studies. I.
On the boundaries of randomization for throughputoptimal scheduling in wireless networks
 In Proc. Allerton Conference on Communication, Control, and Computing (Allerton
, 2010
"... Abstract—It is wellknown that numerous QueueLengthBased (QLB) schedulers, both deterministic and randomized, can achieve the maximum possible throughput region of wireless networks. While randomization is useful in allowing flexibilities in the design and implementation of the schedulers, it may ..."
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Cited by 3 (3 self)
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Abstract—It is wellknown that numerous QueueLengthBased (QLB) schedulers, both deterministic and randomized, can achieve the maximum possible throughput region of wireless networks. While randomization is useful in allowing flexibilities in the design and implementation of the schedulers, it may lead to throughput loss if it is not within limits. In this work, we focus on the N × N inputqueued switch topology to identify the boundaries of randomization in QLB scheduling for achieving throughputoptimality. To that end, we introduce a class of randomized QLB schedulers that are characterized by a wide range of functions. Then, we identify necessary and sufficient conditions on the number of switch ports N and the class of functions that can guarantee throughputoptimality of our class of randomized schedulers. Our results show that while our randomized QLB schedulers are throughputoptimal when N = 2, they cannot be throughputoptimal when N ≥ 3 for a large set of functional forms. For N ≥ 3, we further characterize an achievable rate region described via l2 and l ∞ norms in an N2 dimensional space that extends the existing achievable rate region descriptions. For N = 2, we also study the delay performance of various randomized QLB schedulers through simulations. This preliminary work reveals the sensitivity of throughputoptimal scheduling to the topological characteristics of the network and the functional characteristics of the randomization. I.
ALOHA THAT WORKS
 SUBMITTED TO THE ANNALS OF APPLIED PROBABILITY
"... The popularity of Aloha(like) algorithms for resolution of contention between multiple entities accessing common resources is due to their extreme simplicity and distributed nature. Example applications of such an algorithm include Ethernet and recently emerging wireless multiaccess networks. For ..."
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Cited by 2 (0 self)
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The popularity of Aloha(like) algorithms for resolution of contention between multiple entities accessing common resources is due to their extreme simplicity and distributed nature. Example applications of such an algorithm include Ethernet and recently emerging wireless multiaccess networks. For more than four decades, various researchers have established the inefficiency of (the known versions of) such algorithms to varying degrees in various setups. However, the question that has remained unresolved is that of designing an algorithm that is essentially as simple and distributed as Aloha while being efficient. In this paper, we resolve this question successfully for a network of queues when contention is modeled through independent set constraints over the network graph. The work by Tassiulas and Ephremides (1992) suggests that an algorithm that schedules queues so that the summation of “weight ” of scheduled queues is maximized subject to constraints, is efficient. However, implementing such an algorithm using Aloha like mechanism has remained a mystery. We design such an algorithm building upon a MetropolisHastings sampling mechanism along with selection of “weight ” as an appropriate function of the queue size. The key ingredient in establishing the efficiency of the algorithm is a novel adiabaticlike theorem for the underlying queueing network, which may be of general interest in the context of dynamical systems.
1Optimal Distributed Scheduling under Timevarying Conditions: A FastCSMA Algorithm with Applications
"... Recently, lowcomplexity and distributed Carrier Sense Multiple Access (CSMA)based scheduling algorithms have attracted extensive interest due to their throughputoptimal characteristics in general network topologies. However, these algorithms are not wellsuited for timevarying environments (i.e ..."
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Recently, lowcomplexity and distributed Carrier Sense Multiple Access (CSMA)based scheduling algorithms have attracted extensive interest due to their throughputoptimal characteristics in general network topologies. However, these algorithms are not wellsuited for timevarying environments (i.e., serving realtime traffic under timevarying channel conditions in wireless networks) for two reasons: (1) the mixing time of the underlying CSMA Markov Chain grows with the size of the network, which, for large networks, generates unacceptable delay for deadlineconstrained traffic; (2) since the dynamic CSMA parameters are influenced by the arrival and channel state processes, the underlying CSMA Markov Chain may not converge to a steadystate under strict deadline constraints and fading channel conditions. In this paper, we attack the problem of distributed scheduling for timevarying environments. Specifically, we propose a FastCSMA (FCSMA) policy in fullyconnected topologies, which converges much faster than the existing CSMA algorithms and thus yields significant advantages for timevarying applications. Then, we design optimal policies based on FCSMA techniques in four challenging and important scenarios in wireless networks for scheduling elastic/inelastic traffic with/without channel state information (CSI) over wireless fading channels. I.
ion IEEE/ACM TRANSACTIONS ON NETWORKING 1 Exploring the Throughput Boundaries of Randomized Schedulers in Wireless Networks
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1Crosslayer Optimization for Wireless Networks with Deterministic Channel Models
"... Crosslayer optimization is a key step in wireless network design that coordinates the resources allocated to different layers in order to achieve globally optimal network performance. Existing works on crosslayer optimization for wireless networks often adopt simplistic physicallayer models for w ..."
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Crosslayer optimization is a key step in wireless network design that coordinates the resources allocated to different layers in order to achieve globally optimal network performance. Existing works on crosslayer optimization for wireless networks often adopt simplistic physicallayer models for wireless channels, such as treating interference as noise or interference avoidance. This crude modeling of physical layer often leads to inefficient utilization of resources. In this paper, we adopt a deterministic channel model proposed in [1], [2], a simple abstraction of the physical layer that effectively captures the effect of channel strength, broadcast and superposition in wireless channels. This model allows us to go beyond ”treating interference as noise ” and as a consequence are able to achieve higher throughput and utility. Within the Network Utility Maximization (NUM) framework, we study the crosslayer optimization for wireless networks based on this deterministic channel model. First, we extend the wellstudied conflict graph model to capture the flow interactions over the deterministic channels and characterize the feasible rate region. Then we study distributed algorithms for general wireless multihop networks with both linkcentric formulation and nodecentric formulation. The convergence of algorithms is proved by applying Lyapunov stability theorem and stochastic approximation method. Further, we show the convergence to the bounded neighborhood of optimal solutions with probability one under constant step size and constant update interval. Our numerical evaluations validate the analytical results and show the advantage of deterministic channel model over simple physical layer models such as treating interference as noise. I.
1A FastCSMA Based Distributed Scheduling Algorithm under SINR Model
"... There has been substantial interest over the last decade in developing low complexity decentralized scheduling algorithms in wireless networks. In this context, the queuelength based Carrier Sense Multiple Access (CSMA) scheduling algorithms have attracted significant attention because of their att ..."
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There has been substantial interest over the last decade in developing low complexity decentralized scheduling algorithms in wireless networks. In this context, the queuelength based Carrier Sense Multiple Access (CSMA) scheduling algorithms have attracted significant attention because of their attractive throughput guarantees. However, the CSMA results rely on the mixing of the underlying Markov chain and their performance under fading channel states is unknown. In this work, we formulate a partially decentralized randomized scheduling algorithm for a two transmitter receiver pair set up and investigate its stability properties. Our work is based on the FastCSMA (FCSMA) algorithm first developed in [1] and we extend its results to a signal to interference noise ration(SINR) based interference model in which one or more transmitters can transmit simultaneously while causing interference to the other. In order to improve the performance of the system, we split the traffic arriving at the transmitter into schedule based queues and combine it with the FCSMA based scheduling algorithm. We theoretically examine the performance our algorithm in both nonfading and fading environment and characterize the set of arrival rates which can be stabilized by our proposed algorithm.