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

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Listed:
  • 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
    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. Cohen, J. W., 1974. "Superimposed renewal processes and storage with gradual input," Stochastic Processes and their Applications, Elsevier, vol. 2(1), pages 31-57, January.
    3. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    4. de Vries, C.G., 1990. "On the relation between GARCH and stable processes," Other publications TiSEM d62fff49-1d73-4806-beed-8, Tilburg University, School of Economics and Management.
    5. de Vries, Casper G., 1991. "On the relation between GARCH and stable processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 313-324, June.
    6. Hols, Martien C A B & de Vries, Casper G, 1991. "The Limiting Distribution of Extremal Exchange Rate Returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(3), pages 287-302, July-Sept.
    7. Resnick, Sidney I., 1997. "Discussion of the Danish Data on Large Fire Insurance Losses," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 139-151, May.
    8. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
    9. David Heath & Sidney Resnick & Gennady Samorodnitsky, 1998. "Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models," Mathematics of Operations Research, INFORMS, vol. 23(1), pages 145-165, February.
    10. de Vries, C.G., 1991. "On the relation between GARCH and stable processes," Other publications TiSEM 6e9f0b15-627b-4b3d-9ca4-8, Tilburg University, School of Economics and Management.
    11. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
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