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Heavy traffic methods in wireless systems: towards modeling heavy tails and long range dependence. (English) Zbl 1131.93376

Agrawal, Prathima (ed.) et al., Wirelesse communications. Invited papers based on the presentations at the IMA summer school program on wireless communications, University of Minnesota, June 22 – July 1, 2005. New York, NY: Springer (ISBN 0-387-37269-5/hbk). The IMA Volumes in Mathematics and its Applications 143, 53-74 (2007).
Summary: 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 [R. Buche and J. J. Kushner, IEEE Transactions on Automatic Control, 47(6), 992–1003 (2002)]. At the same time, similarly to what happened for wireline networks, the emergence of high capacity ap- plications (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 assump- tions 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 Lévy 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 T. G. Kurtz, Networks: Theory and Applications, 119–139 (1996)], are described. The corresponding heavy traffic model is now driven by fractional Brownian motion. As stochastic control analysis for stable Lévy motion or fractional Brownian motion is currently undeveloped, the queue limit models character- izing the wireless system can be studied only under given controls, such as stabilizing controls or else heuristic policies.
For the entire collection see [Zbl 1104.90301].

MSC:

93E03 Stochastic systems in control theory (general)
60G18 Self-similar stochastic processes
60G51 Processes with independent increments; Lévy processes
60G57 Random measures
90B18 Communication networks in operations research
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