Heavy Traffic Analysis for A Multiplexer Driven by M/GI/infinity Input Processes
MARYLAND UNIV COLLEGE PARK INST FOR SYSTEMS RESEARCH
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We study the heavy traffic regime of a multiplexer driven by correlated inputs, namely the M GI infinity input processes of Cox. We distinguish between M GI infinity processes exhibiting short or long-range dependence, identifying for each case the appropriate heavy traffic scaling that results in non-degenerate limits. As expected, the limits we obtain for short-range dependent inputs involve the standard Brownian motion. Of particular interest though are our conclusions for the long-range dependent case The normalized queue length can be expressed as a function not of a fractional Brownian motion, but of some other stable non-Gaussian self-similar process. Thus, the M G infinity processes serve as an example demonstrating that, within long-range dependence, fractional Brownian motion does not assume the ubiquitous role that its counterpart, standard Brownian motion, plays in the short-range dependence setup, and that modeling possibilities attracted to non-Gaussian limits are not so hard to come by.
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