Understanding the Capacity Region of the Greedy Maximal Scheduling Algorithm in Multi-Hop Wireless Networks

Abstract

Abstract-In this paper, we characterize the performance of an important class of scheduling schemes, called Greedy Maximal Scheduling (GMS), for multi-hop wireless networks. While a lower bound on the throughput performance of GMS is relatively well-known in the simple node-exclusive interference model, it has not been thoroughly explored in the more general K-hop interference model. Moreover, empirical observations suggest that the known bounds are quite loose, and that the performance of GMS is often close to optimal. In this paper, we provide a number of new analytic results characterizing the performance limits of GMS. We first provide an equivalent characterization of the efficiency ratio of GMS through a topological property called the local-pooling factor of the network graph. We then develop an iterative procedure to estimate the local-pooling factor under a large class of network topologies and interference models. We use these results to study the worst-case efficiency ratio of GMS on two classes of network topologies. First, we show how these results can be applied to tree networks to prove that GMS achieves the full capacity region in tree networks under the K-hop interference model. Second, we show that the worst-case efficiency ratio of GMS in geometric network graphs is between 1 6 and 1 3 .

A High-Order Markov-Chain-Based Scheduling Algorithm for Low Delay in CSMA Networks

“…In other words, in our high-order Markov-chain-based approach, while the stationary distribution of the schedule itself remains untouched and it provides better queueing performance in the steady state, it may take roughly times longer to reach the steady state. 2 This tradeoff between a bit slower convergence but to a "better" stationary regime also implies that the performance during the transient phase can be worse than that of the conventional CSMA algorithm (albeit our algorithm will eventually pay off in the end) and necessitates a careful choice of depending upon how long the system is meant to be running.…”

“…The MWS, however, is not deemed practical since it requires global information to solve a complicated combinatorial optimization problem in each time instance. Many heuristics such as greedy-maximal scheduling (GMS) or maximal-matching algorithms are considered as alternatives to MWS, but they may achieve only a fraction of the capacity region [2], [3], or are throughput-optimal only on certain types of network topology [4]- [6]. There are also several methodologies for achieving the throughput optimality in a general network [7]- [9], but they have turned out to incur excessive message passing in many cases.…”

Low complexity stable link scheduling for maximizing throughput in wireless networks

“…They prove that their algorithm achieves k k+2 of the capacity region, for every k ≥ 1. In [9], Joo developed a simple distributed scheduling policy that achieves O(log |V |) complexity by relaxing the global ordering requirement of Greedy Maximal Scheduling (GMS) [10]. It deterministically schedules only links that have the largest queue lengths among their local neighbors.…”

Distributed Throughput Maximization in Wireless Networks via Random Power Allocation

“…Hence, in multi-hop wireless networks, it may be impractical to find its solution in every time slot due to limited computation capability, and the need for distributed operation. As an alternative, distributed greedy scheduling has been proposed and analyzed [7], [17], [19], [20], [21]. However, most of the existing works in this context adopt the graph-based interference models, where transmissions on any two links in the network are assumed to be either in conflict or conflict-free.…”