Heavy Traffic Limits Associated With M/GI/infinity Input Processes
Technical research rept.
MARYLAND UNIV COLLEGE PARK INST FOR SYSTEMS RESEARCH
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We study the heavy traffic regime of a discrete time queue driven by correlated inputs, namely the MGI infinity input processes of Cox. We distinguish between MGI infinity processes with short- and 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 are the 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 an OL stable, io self-similar independent increments Levy process. The resulting buffer asymptotics in heavy traffic display a hyperbolic decay, of power 1-alpha. Thus, MGI infinity processes already demonstrate that, within long range dependence, fractional Brownian motion does not necessarily assume the ubiquitous role that standard Brownian motion plays in the short range dependence setup.
- Physical Chemistry
- Computer Systems Management and Standards