Spatial inefficiency of MaxWeight scheduling

Abstract

Abstract-MaxWeight scheduling has gained enormous popularity as a powerful paradigm for achieving queue stability and maximum throughput in a wide variety of scenarios. The maximum-stability guarantees however rely on the fundamental premise that the system consists of a fixed set of flows with stationary ergodic traffic processes. In the present paper we examine networks where the population of active flows varies over time, as flows eventually end while new flows occasionally start. We show that MaxWeight policies may fail to provide maximum stability due to persistent inefficient spatial reuse. The intuitive explanation is that these policies tend to serve flows with large backlogs, even when the resulting spatial reuse is not particularly efficient, and fail to exploit maximum spatial reuse patterns involving flows with smaller backlogs. These results indicate that instability of MaxWeight scheduling can occur due to spatial inefficiency in networks with fixed transmission rates, which is fundamentally different from the inability to fully exploit timevarying rates shown in prior work. We discuss how the potential instability effects can be countered by spatial traffic aggregation, and describe some of the associated challenges and performance trade-offs.

Exploring the inefficiency and instability of Back-Pressure algorithms

“…The bursty arrivals force Q-BP to distribute the amount of time for each feasible schedule in an inefficient manner, which makes certain "regions" (e.g., links (2, 4) and (4, 6)) receive insufficient amount of service. This type of inefficiency is similar to the inefficient spatial reuse identified in [9] for single-hop traffic.…”

“…Interestingly, the work of [9] provides another set of counterexamples to show that even without rate variations, instability of the MaxWeight algorithm can still occur, due to inefficient spatial reuse. This reveals that channel fading and rate variations are not the only causes of inefficiency and instability associated with flow-level dynamics.…”

“…This reveals that channel fading and rate variations are not the only causes of inefficiency and instability associated with flow-level dynamics. Further, since the solutions in [5]- [8] cannot be easily extended to the settings considered in [9], the authors develop a region-based MaxWeight scheduling algorithm to counter the instability effects. In the region-based MaxWeight algorithm, the entire network is partitioned into a finite number of regions.…”

“…In each time-slot, the algorithm selects a subset of non-interfering regions based on the aggregate backlog in each region, and then serves a flow in each selected region. However, as mentioned by the authors themselves in [9], it is quite difficult for their solution to identify an adequate number of regions, without explicit knowledge of the traffic parameters.…”

“…First, we focus on the inefficiency and instability in the settings of multihop traffic with fixed routes, and present two counterexamples to show that both queue-length-based and delay-based Back-Pressure algorithm may fail to guarantee stability in the presence of flow-level dynamics. The essential cause of the instability comes from inefficient schedule reuse, which is similar to the spatial inefficiency identified in [9]. Second, we focus on a wireless downlink system where relay-assisted 2-hop communications can be adopted to improve throughput performance.…”