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Mean queue size in a queue with discrete autoregressive arrivals of order p

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  • Jeongsim Kim
  • Bara Kim
  • Khosrow Sohraby

Abstract

We consider a discrete time single server queueing system where the arrival process is governed by a discrete autoregressive process of order p (DAR(p)), and the service time of a customer is one slot. For this queueing system, we give an expression for the mean queue size, which yields upper and lower bounds for the mean queue size. Further we propose two approximation methods for the mean queue size. One is based on the matrix analytic method and the other is based on simulation. We show, by illustrations, that the proposed approximations are very accurate and computationally efficient. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Jeongsim Kim & Bara Kim & Khosrow Sohraby, 2008. "Mean queue size in a queue with discrete autoregressive arrivals of order p," Annals of Operations Research, Springer, vol. 162(1), pages 69-83, September.
    • Handle: RePEc:spr:annopr:v:162:y:2008:i:1:p:69-83:10.1007/s10479-008-0318-1
    DOI: 10.1007/s10479-008-0318-1
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    References listed on IDEAS

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    1. Dehnert, M. & Helm, W.E. & Hütt, M.-Th., 2003. "A discrete autoregressive process as a model for short-range correlations in DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 327(3), pages 535-553.
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    Cited by:

    1. Herwig Bruneel & Dieter Fiems & Joris Walraevens & Sabine Wittevrongel, 2014. "Queueing models for the analysis of communication systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 421-448, July.

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