On the queue-overflow probabilities of distributed scheduling algorithms

• Published in: Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference pp. 4820 - 4825
• Main Authors: Can Zhao, Xiaojun Lin
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2009
• Subjects: Algorithm design and analysis; Delay; H infinity control; Probability; Queueing analysis; Scheduling algorithm; Stability criteria; Statistics; Streaming media; Wireless networks
• ISBN: 9781424438716; 1424438713
• ISSN: 0191-2216
• DOI: 10.1109/CDC.2009.5399662

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.