Towards heavy traffic models for wireless queueing systems incorporating heavy tails and long range dependence
by
Robert Buche
NC State University, Department of Applied Mathematics
Coauthors: Jim X. Zhang, NC State University, Department of Applied Mathematics

Heavy tailed/long range dependent (LRD) models are important for high speed networks and there has be a focus on the asymptotics, under a central-limit-theorem-like scaling, of the arrival processes, under a constant transmission rate assumption. The limit models satisfied by the arrival process have been shown to converge to fractional Brownian motion (fBm) or else an alpha-stable Lévy process. We will outline some directions and challenges for extending these results to a wireless queueing model, under a heavy traffic framework (essentially, heavy traffic means the system is operating a near capacity), where the objective is to obtain a limit model for the queue-size process. Brownian driven limit models for wireless applications have been obtained (and this will be outlined), but there are new challenges in obtaining (the expected) fBm and alpha-stable Lévy limit models under heavy tails and LRD assumptions. Furthermore, for the wireless model to be useful, one has to account for the stochastic variations in the transmission rates due to the constantly changing environment.

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Date received: October 15, 2005