On the queue-overflow probabilities of distributed scheduling algorithms - Can Zhao; Xiaojun Lin (Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009)
In this paper, we are interested in using large-deviations theory to characterize the asymptotic decay-rate of the queue-overflow probability for distributed wireless scheduling algorithms, as the overflow threshold approaches infinity. We consider ad-hoc wireless networks where each link interferes with a given set of other links, and we focus on a distributed scheduling algorithm called Q-SCHED, which is introduced by Gupta et al. First, we derive a lower bound on the asymptotic decay rate of the queue-overflow probability for Q-SCHED. We then present an upper bound on the decay rate for all possible algorithms operating on the same network. Finally, using these bounds, we are able to conclude that, subject to a given constraint on the asymptotic decay rate of the queue-overflow probability, Q-SCHED can support a provable fraction of the offered loads achievable by any algorithms.