Fluid queues with heavy-tailed M/G/∞ input

Fluid queues with heavy-tailed M/G/∞ input

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Article ID: iaor20061435
Country: United States
Volume: 30
Issue: 4
Start Page Number: 852
End Page Number: 879
Publication Date: Nov 2005
Journal: Mathematics of Operations Research
Authors: ,
Keywords: M/G/infinity queues
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.

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