Large Deviations Sum-Queue Optimality of a Radial Sum-Rate Monotone Opportunistic Scheduler

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 monotonic (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.