Heavy Traffic Methods in Wireless Systems: Towards Modeling Heavy Tails and Long Range Dependence

Heavy traffic models for wireless queueing systems under short range dependence and light tail assumptions on the data traffic have been studied recently. We outline one such model considered by Buche and Kushner [7]. At the same time, similarly to what happened for wireline networks, the emergence of high capacity applications (multimedia, gaming) and inherent mechanisms (multi-access interference) of wireless networks have led to the growing evidence of long range dependence and heavy tail characteristics in data traffic. Extending heavy traffic methods under these assumptions presents significant challenges. We discuss an approach for extending the methods in [7] under a heavy tail assumption only. The corresponding heavy traffic model is based on (non-Gaussian) stable Levy motion, not Brownian motion which is associated with a light tail assumption. When long range dependence is also present, a promising alternative approach and model based on a Poisson measure representation, motivated from Kurtz [17], are described. The corresponding heavy traffic model is now driven by fractional Brownian motion. As stochastic control analysis for stable Levy motion or fractional Brownian motion is currently undeveloped, the queue limit models characterizing the wireless system can be studied only under given controls, such as stabilizing controls or else heuristic policies.