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Performance Decay in a Single Server Exponential Queueing Model with Long Range Dependence

Author

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  • Sidney Resnick

    (Cornell University, Ithaca, New York)

  • Gennady Samorodnitsky

    (Cornell University, Ithaca, New York)

Abstract

We discuss how long-range dependence can influence the characteristics of a single server queue. We take the analogue of the G / M /1 queue except that the input stream is altered to exhibit long-range dependence. The equilibrium queue size and equilibrium waiting time distributions have heavy tails. By suitably selecting the parameters of the inputs, the queue size or waiting time can be made to possess infinite variance and even infinite mean. Some simulations dramatically illustrate the potential for undetected long-range dependence to significantly alter the queueing behavior compared to what is anticipated with traditional inputs.

Suggested Citation

  • Sidney Resnick & Gennady Samorodnitsky, 1997. "Performance Decay in a Single Server Exponential Queueing Model with Long Range Dependence," Operations Research, INFORMS, vol. 45(2), pages 235-243, April.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:2:p:235-243
    DOI: 10.1287/opre.45.2.235
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    Citations

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    Cited by:

    1. Robert, Christian Y. & Segers, Johan, 2008. "Tails of random sums of a heavy-tailed number of light-tailed terms," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 85-92, August.
    2. Civelek, Ismail & Biller, Bahar & Scheller-Wolf, Alan, 2021. "Impact of dependence on single-server queueing systems," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1031-1045.
    3. Petra Tomanová & Vladimír Holý, 2021. "Clustering of arrivals in queueing systems: autoregressive conditional duration approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 859-874, September.
    4. Nima Manafzadeh Dizbin & Barış Tan, 2019. "Modelling and analysis of the impact of correlated inter-event data on production control using Markovian arrival processes," Flexible Services and Manufacturing Journal, Springer, vol. 31(4), pages 1042-1076, December.
    5. 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.
    6. Christian Y. Robert & Johan Segers, 2007. "Tails of random sums of a heavy-tailed number of light-tailed terms," Papers math/0703022, arXiv.org, revised Oct 2007.

    More about this item

    Keywords

    queues; with serially correlated input;

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