Macroscopic models for long-range dependent network traffic |
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Authors: | Konstantopoulos Takis Lin Si-Jian |
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Institution: | (1) Department of Electrical and Computer Engineering, University of Texas, Austin, TX 78712, USA |
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Abstract: | A common way to inject long-range dependence in a stochastic traffic model possessing a weak regenerative structure is to
make the variance of the underlying period infinite (while keeping the mean finite). This method is supported both by physical
reasoning and by experimental evidence. We exhibit the long-range dependence of such a process and, by studying its second-order
properties, we asymptotically match its correlation structure to that of a fractional Brownian motion. By studying a certain
distributional limit theorem associated with such a process, we explain the emergence of an extremely skewed stable Lévy motion
as a macroscopic model for the aforementioned traffic. Surprisingly, long-range dependence vanishes in the limit, being “replaced”
by independent increments and highly varying marginals. The marginal distribution is computed and is shown to match the one
empirically obtained in practice. Results on performance of queueing systems with Lévy inputs of the aforementioned type are
also reported in this paper: they are shown to be in agreement with pre-limiting models, without violating experimental queueing
analysis.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | long-range dependence Lévy processes traffic modeling performance evaluation self-similarity regular variation |
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