Large deviations sum-queue optimality of a radial sum-rate monotone opportunistic scheduler

TL;DR

This paper introduces a radial sum-rate monotone (RSM) scheduler called p-Log Rule for wireless systems, demonstrating its throughput optimality and superior large deviations performance in maximizing the decay rate of the sum-queue distribution.

Contribution

It proposes and analyzes the p-Log RSM scheduler, showing it outperforms traditional schedulers by maximizing the sum-queue decay rate, thus offering robustness in heterogeneous wireless environments.

Findings

p-Log Rule is throughput-optimal.

p-Log Rule maximizes the asymptotic exponential decay rate of the sum-queue.

RSM schedulers are effective for robust wireless system design.

Abstract

A centralized wireless system is considered that is serving a fixed set of users with time varying channel capacities. An opportunistic scheduling rule in this context selects a user (or users) to serve based on the current channel state and user queues. Unless the user traffic is symmetric and/or the underlying capacity region a polymatroid, little is known concerning how performance optimal schedulers should tradeoff "maximizing current service rate" (being opportunistic) versus "balancing unequal queues" (enhancing user-diversity to enable future high service rate opportunities). By contrast with currently proposed opportunistic schedulers, e.g., MaxWeight and Exp Rule, a radial sum-rate monotone (RSM) scheduler de-emphasizes queue-balancing in favor of greedily maximizing the system service rate as the queue-lengths are scaled up linearly. In this paper it is shown that an RSM opportunistic scheduler, p-Log Rule, is not only throughput-optimal, but also maximizes the asymptotic exponential decay rate of the sum-queue distribution for a two-queue system. The result complements existing optimality results for opportunistic scheduling and point to RSM schedulers as a good design choice given the need for robustness in wireless systems with both heterogeneity and high degree of uncertainty.