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

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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)

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).

Suggested Citation

  • Sidney Resnick & Gennady Samorodnitsky, 2000. "A Heavy Traffic Approximation for Workload Processes with Heavy Tailed Service Requirements," Management Science, INFORMS, vol. 46(9), pages 1236-1248, September.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:9:p:1236-1248
    DOI: 10.1287/mnsc.46.9.1236.12234
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    References listed on IDEAS

    as
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