On the queue-overflow probabilities of a class of distributed scheduling algorithms

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.