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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.
Complexity in wireless scheduling: Impact and tradeoffs
 in Proceedings of ACM Mobihoc, Hong Kong
, 2008
"... It has been an important research topic since 1992 to maximize stability region in constrained queueing systems, which includes the study of scheduling over wireless ad hoc networks. In this paper, we propose a framework to study a wide range of existing and future scheduling algorithms and characte ..."
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Cited by 21 (8 self)
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It has been an important research topic since 1992 to maximize stability region in constrained queueing systems, which includes the study of scheduling over wireless ad hoc networks. In this paper, we propose a framework to study a wide range of existing and future scheduling algorithms and characterize the achieved tradeoffs in stability, delay, and complexity. These characterizations reveal interesting properties hidden in the study of any one or two dimensions in isolation. For example, decreasing complexity from exponential to polynomial, while keeping stability region the same, generally comes at the expense of exponential growth of delays. Investigating tradeoffs in the 3dimensional space allows a designer to fix one dimension and vary the other two jointly. For example, incentives for using scheduling algorithms with only partial throughputguarantee can be quantified with regards to delay and complexity. Tradeoff analysis is then extended to systems with congestion control through utility maximization for nonstabilizable arrival inputs, where the complexityutilitydelay tradeoff is shown to be different from the complexitystabilitydelay tradeoff. Finally, we analyze more practical models with bounded message size, and consider “effective throughput” which reflects resource occupied by control messages. We show that effective throughput may degrade significantly in certain scheduling algorithms, and suggest a mechanism to avoid this problem in light of the 3D tradeoff framework.
Message Passing for Maximum Weight Independent Set
"... Abstract—In this paper, we investigate the use of messagepassing algorithms for the problem of finding the maxweight independent set (MWIS) in a graph. First, we study the performance of the classical loopy maxproduct belief propagation. We show that each fixedpoint estimate of max product can be ..."
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Cited by 18 (2 self)
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Abstract—In this paper, we investigate the use of messagepassing algorithms for the problem of finding the maxweight independent set (MWIS) in a graph. First, we study the performance of the classical loopy maxproduct belief propagation. We show that each fixedpoint estimate of max product can be mapped in a natural way to an extreme point of the linear programming (LP) polytope associated with the MWIS problem. However, this extreme point may not be the one that maximizes the value of node weights; the particular extreme point at final convergence depends on the initialization of max product. We then show that if max product is started from the natural initialization of uninformative messages, it always solves the correct LP, if it converges. This result is obtained via a direct analysis of the iterative algorithm, and cannot be obtained by looking only at fixed points. The tightness of the LP relaxation is thus necessary for maxproduct optimality, but it is not sufficient. Motivated by this observation, we show that a simple modification of max product becomes gradient descent on (a smoothed version of) the dual of the LP, and converges to the dual optimum. We also develop a messagepassing algorithm that recovers the primal MWIS solution from the output of the descent algorithm. We show that the MWIS estimate obtained using these two algorithms in conjunction is correct when the graph is bipartite and the MWIS is unique. Finally, we show that any problem of maximum a posteriori (MAP) estimation for probability distributions over finite domains can be reduced to an MWIS problem. We believe this reduction will yield new insights and algorithms for MAP estimation. Index Terms—Belief propagation, combinatorial optimization, distributed algorithms, independent set, iterative algorithms, linear programming (LP), optimization.
Distributed CrossLayer Algorithms for the Optimal Control of Multihop Wireless Networks
"... In this paper, we provide and study a general framework that facilitates the development of distributed mechanisms to achieve full utilization of multihop wireless networks. In particular, we describe a generic randomized routing, scheduling and flow control scheme that allows for a set of imperf ..."
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Cited by 18 (8 self)
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In this paper, we provide and study a general framework that facilitates the development of distributed mechanisms to achieve full utilization of multihop wireless networks. In particular, we describe a generic randomized routing, scheduling and flow control scheme that allows for a set of imperfections in the operation of the randomized scheduler to account for potential errors in its operation. These imperfections enable the design of a large class of lowcomplexity and distributed implementations for different interference models. We study the effect of such imperfections on the stability and fairness characteristics of the system, and explicitly characterize the degree of fairness achieved as a function of the level of imperfections. Our results reveal the relative importance of different types of errors on the overall system performance, and provide valuable insight to the design of distributed controllers with favorable fairness characteristics. In the second part of the paper, we focus on a specific interference model, namely the secondary interference model, and develop distributed algorithms with polynomial communication and computation complexity in the network size. This is an important result given that earlier centralized throughputoptimal algorithms developed for such a model relies on the solution to an NPhard problem at every decision. This results in a polynomial complexity crosslayer algorithm that achieves throughput optimality and fair allocation of network resources amongst the users. We further show that our algorithmic approach enables us to efficiently approximate the capacity region of a multihop wireless network.
Stochastic Network Utility Maximization A tribute to Kelly’s paper published in this journal a decade ago
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Wireless scheduling algorithms with O(1) complexity for Mhop interference model
, 2007
"... Abstract—We develop a family of distributed wireless scheduling algorithms that requires only O(1) complexity for Mhop interference model, for any finite M. The recent technology advances and heterogeneity in wireless networks lead to various interference patterns. Thus, a scheduling algorithm gear ..."
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Cited by 10 (0 self)
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Abstract—We develop a family of distributed wireless scheduling algorithms that requires only O(1) complexity for Mhop interference model, for any finite M. The recent technology advances and heterogeneity in wireless networks lead to various interference patterns. Thus, a scheduling algorithm geared into a specific interference model (typically onehop or twohop in literature) may be limited in its applicability. In this paper, we tackle this problem, and develop a family of scheduling algorithms (which guarantees throughput and delay performance) for Mhop interference models. To achieve such a goal, we use the concept of vertex augmentation, and for a given M, the family of parameterized algorithms are proposed and the tradeoffs among throughput, complexity, and delay are studied.
Hardness of low delay network scheduling ∗
, 2009
"... We consider a communication network and study the problem of designing a highthroughput and lowdelay scheduling policy that only requires a polynomial amount of computation at each time step. The wellknown maximum weight scheduling policy, proposed by Tassiulas and Ephremides (1992), has favorable ..."
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Cited by 8 (0 self)
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We consider a communication network and study the problem of designing a highthroughput and lowdelay scheduling policy that only requires a polynomial amount of computation at each time step. The wellknown maximum weight scheduling policy, proposed by Tassiulas and Ephremides (1992), has favorable performance in terms of throughput and delay but, for general networks, it can be computationally very expensive. A related randomized policy proposed by Tassiulas (1998) provides maximal throughput with only a small amount of computation per step, but seems to induce exponentially large average delay. These considerations raise some natural questions. Is it possible to design a policy with low complexity, high throughput, and low delay for a general network? Does Tassiulas ’ randomized policy result in low average delay? In this paper, we answer both of these questions negatively. We consider a wireless network operating under two alternative interference models: (a) a combinatorial model involving independent set constraints; and (b) the standard SINR (signal to interference noise ratio) model. We show that unless NP⊆BPP (or P=NP for the case of determistic arrivals and deterministic policies), and even if the required throughput is a very small fraction of the network’s capacity, there does not exist a lowdelay policy whose computation per time step scales polynomially with the number of queues. In particular, the average delay of Tassiulas ’ randomized algorithm must grow superpolynomially. To establish our results, we employ a clever graph transformation introduced by Lund and Yannakakis (1994).
Feasible rate allocation in wireless networks
"... Abstract—Rate allocation is a fundamental problem in the operation of a wireless network because of the necessity to schedule the operation of mutually interfering links between the nodes. Among the many reasons behind the importance of efficiently determining the membership of an arbitrary rate vec ..."
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Cited by 7 (3 self)
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Abstract—Rate allocation is a fundamental problem in the operation of a wireless network because of the necessity to schedule the operation of mutually interfering links between the nodes. Among the many reasons behind the importance of efficiently determining the membership of an arbitrary rate vector in the feasibility region, is its high relevance in optimal cross layer design. A key feature in a wireless network is that links without common nodes can also conflict (secondary interference constraints). While the node exclusive model problem has efficient algorithms [8], it has long been known that this is a hard problem with these additional secondary constraints [1]. However, wireless networks are usually deployed in geographic areas that do not span the most general class of all graphs possible. This is the underlying theme of this paper, where we provide algorithms for two restricted instances of wireless network topologies. In the first tractable instance, we consider nodes placed arbitrarily in a region such that (a) the node density is bounded, and (b) a node can only transmit or interfere with other nodes that are within a certain limited radius. We obtain a simple (1 − ε) polynomialtime approximation scheme for checking feasibility (for any ε> 0). The second instance considers the membership problem of an arbitrary ratevector in the feasible set, where the nodes are distributed within a slab of fixed width (there are no density assumptions). Specifically, the results in [12] are shown to extend to a much more general class of graphs, which we call the (dmin, dmax) class of graphs, and this generalization is used to obtain a strongly polynomial time algorithm that decides membership of a ratevector where the hosts are distributed within an infinite corridor with fixed crosssection. I.
Delay Guarantees for Throughputoptimal Wireless Link Scheduling
"... Abstract—We consider the question of obtaining tight delay guarantees for throughoutoptimal link scheduling in arbitrary topology wireless adhoc networks. We consider two classes of scheduling policies: 1) a maximum queuelength weighted independent set scheduling policy, and 2) a randomized indep ..."
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Cited by 7 (1 self)
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Abstract—We consider the question of obtaining tight delay guarantees for throughoutoptimal link scheduling in arbitrary topology wireless adhoc networks. We consider two classes of scheduling policies: 1) a maximum queuelength weighted independent set scheduling policy, and 2) a randomized independent set scheduling policy where the independent set scheduling probabilities are selected optimally. Both policies stabilize all queues for any set of feasible packet arrival rates, and are therefore throughputoptimal. For these policies and i.i.d. packet arrivals, we show that the average packet delay is bounded by a constant that depends on the chromatic number of the interference graph, and the overall load on the network. We also prove that this upper bound is asymptotically tight in the sense that there exist classes of topologies where the expected delay attained by any scheduling policy is lower bounded by the same constant. Through simulations we examine the scaling of the average packet delay with respect to the overall load on the network, and the chromatic number of the link interference graph. I.
Delay and Effective Throughput of Wireless Scheduling in Heavy Traffic Regimes: Vacation Model for Complexity
"... Distributed scheduling algorithms for wireless ad hoc networks have received substantial attention over the last decade. The complexity levels of these algorithms span a wide spectrum, ranging from no message passing to constant/polynomial time complexity, or even exponential complexity. However, by ..."
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Cited by 5 (3 self)
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Distributed scheduling algorithms for wireless ad hoc networks have received substantial attention over the last decade. The complexity levels of these algorithms span a wide spectrum, ranging from no message passing to constant/polynomial time complexity, or even exponential complexity. However, by and large it remains open to quantify the impact of message passing complexity on throughput and delay. In this paper, we study the effective throughput and delay performance in wireless scheduling by explicitly considering complexity through a vacation model, where signaling complexity is treated as “vacations ” and data transmissions as “services,” with a focus on delay analysis in heavy traffic regimes. We analyze delay performance in two regimes of vacation models, depending on the relative lengths of data transmission and vacation periods. State space collapse properties proved here enable a significant dimensionality reduction in the challenging problem of delay characterization. We then explore engineering implications and quantify intuitions based on the heavy traffic analysis.