ISyE Seminar Series - Long Range Dependency and Subexponential Tail Distributions

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Long range dependence and heavy tail distribution have been reported in a number of studies of Internet and Web traffic during the last decade. It is widely believed that Web traffic exhibits heavy tail distributions and is one of the major causes of long range dependence observed in the Internet traffic. In this talk, we re-examine these issues and provide some new insights. In particular, we show that such heavy tail distributions are not the most appropriate for characterizing traffic of many Web servers. Instead, lighter but subexponential tail distributions are frequently observed which can not cause long range dependence, yet coexist with the long range dependence in the observation.

We then analyze the asymptotic tail distribution of stationary waiting times and stationary virtual waiting times in a single server queue with long-range dependent arrival process and subexponential service times. We investigate the joint impact of the long range dependency of the arrival process and of the tail distribution of the service times. We consider two traffic models that have been widely used to characterize the long-range dependence structure, namely, the fractional Gaussian noise (FGN) model and the M/G/infty input model. We show that the asymptotic tail distribution of the waiting time is dominated by either the arrival process or the service times, depending on how large is the Hurst parameter of the
arrival process compared to the service time distribution.

This is joint work with Cathy Xia at IBM Research.


  • Workflow Status: Published
  • Created By: Barbara Christopher
  • Created: 10/08/2010
  • Modified By: Fletcher Moore
  • Modified: 10/07/2016


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