Fluid Queues with Heavy-Tailed M/G/∞ Input

Authors:
Sem Borst;Bert Zwart
Affiliations:
CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands, and Bell Laboratories, Lucent Technologies, P.O. Box 636, Murray Hill, NJ 07974-0636;Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Venue:
Mathematics of Operations Research
Year:
2005

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Abstract

We consider a fluid queue fed by several heterogeneous M/G/∞ input processes with regularly varying session lengths. Under fairly mild assumptions, we derive the exact asymptotic behavior of the stationary workload distribution. In addition, we obtain several asymptotic results for the transient workload distribution, which are applied to obtain a conditional limit theorem for the most probable time to overflow. The results are strongly inspired by the large-deviations idea that overflow is typically due to some minimal combination of extremely long concurrent sessions causing positive drift. The typical configuration of long sessions is identified through a simple integer program, paving the way for the exact computation of the asymptotic workload behavior. The calculations provide crucial insight in the typical overflow scenario.