A Heavy Traffic Approximation for Workload Processes with Heavy Tailed Service Requirements

Sidney Resnick () and Gennady Samorodnitsky ()
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Sidney Resnick: School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853
Gennady Samorodnitsky: School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853

Management Science, 2000, vol. 46, issue 9, 1236-1248

Abstract: A system with heavy tailed service requirements under heavy load having a single server has an equilibrium waiting time distribution which is approximated by the Mittag-Leffler distribution. This fact is understood by a direct analysis of the weak convergence of a sequence of negative drift random walks with heavy right tail and the associated all time maxima of these random walks. This approach complements the recent transform view of Boxma and Cohen (1997).

Keywords: heavy tails; regular variation; pareto tails; heavy traffic approximation; random walk; queueing (search for similar items in EconPapers)
Date: 2000
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