Delay Guarantees for Throughput-Optimal Wireless Link Scheduling

Abstract

Abstract-We consider the question of obtaining tight delay guarantees for throughout-optimal link scheduling in arbitrary topology wireless ad-hoc networks. We consider two classes of scheduling policies: 1) a maximum queue-length 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 throughput-optimal. 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.

The case for addressing the limiting impact of interference on wireless scheduling

“…They include LQF and its variants [7], [8], [25], [9], GreedyPhysical and its variants [10], [11], as well as LengthDiversity [5]. The throughput and delay performance [26], [27] as well as the distributed implementation [26], [28] of these algorithms have also been studied, and scheduling based on dominant interferers has been considered by Badia et al [25]. Nonetheless, these work have not focused on the impact of link ordering on interferencelimited scheduling; the analysis of these algorithms has also mostly focused on the asymptotic behavior without characterizing the impact of potentially large constants in the analysis.…”

Delay-Constrained Optimal Link Scheduling in Wireless Sensor Networks

“…In this model, arcs in a conflict graph connect nodes, which represent the links (in the wireless network) that can not transmit simultaneously due to mutual interference. Actually, for the joint routing and link scheduling problem, it can be formulated as a graph coloring problem, since wireless contentions can be modeled by conflict graphs and moreover, coloring on a conflict graph is equivalent to finding a set of independent sets with appropriate cardinality [13] which leads to a conflict-free schedule [14] [15]. In Ref.…”

“…In addition, Ref. [15] showed the scaling of the average packet delay with respect to the overall load on the network and the chromatic number of the link conflict graph; and in Ref. [19], the authors also studied the delay performance and proposed a linear integer programming formulation for the link scheduling problem in TDM wireless mesh networks under a sink-tree topology and constant bit rate traffic.…”

Approximation algorithms for throughput maximization in wireless networks with delay constraints

“…While there has been much work on delay-throughput trade-offs, especially for random networks or restricted 1-hop sessions, the best results for average end-to-end delay bounds known so far considering scheduling with fixed routes and traffic rates are by [25], [22], [24], [28]. Kar et al [25] study both max-weight and randomized independent set scheduling policies, and show that the average packet delay is bounded by the chromatic number C(N ) of the interference graph; C(N ) represents the minimum number of independent sets into which the link conflict graph of a network N can be partitioned.…”

“…Kar et al [25] study both max-weight and randomized independent set scheduling policies, and show that the average packet delay is bounded by the chromatic number C(N ) of the interference graph; C(N ) represents the minimum number of independent sets into which the link conflict graph of a network N can be partitioned. Jagabathula and Shah [22] design a scheduling scheme that ensures per-session end-toend delays of O (#hops) with the total throughput within a constant factor of the optimum; however, this result is restricted to primary interference, whereas for general graphbased interference, the delay bound becomes O #hops · D 2 , where D denotes the maximum degree in the conflict graph (which could be high).…”