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Relations between the prearrival and postdeparture state probabilities and the fcfs waiting time distribution in the Ek/G/s queue

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  • Xenophon Papaconstantinou
  • Dimitris Bertsimas

Abstract

We generalize a theorem by Burke concerning the relations between the prearrival and the postdeparture state probabilities and we establish the relation of the postdeparture probabilities and the FCFS waiting time distribution in the Ek/G/s queue. Based on these results, an exact probabilistic method for the explicit evaluation of the stationary FCFS waiting time distribution of the Ek/G/s queue is offered. By exploiting previous analytic results of the authors, this method is applied to the general Coxian class of service time distributions with rational Laplace transform and leads to closed form expressions involving linear combinations of a finite number of exponential terms. Finally some computational results are presented.

Suggested Citation

  • Xenophon Papaconstantinou & Dimitris Bertsimas, 1990. "Relations between the prearrival and postdeparture state probabilities and the fcfs waiting time distribution in the Ek/G/s queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(1), pages 135-149, February.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:1:p:135-149
    DOI: 10.1002/1520-6750(199002)37:13.0.CO;2-F
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    References listed on IDEAS

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    1. Paul J. Burke, 1956. "The Output of a Queuing System," Operations Research, INFORMS, vol. 4(6), pages 699-704, December.
    2. Bertsimas, Dimitris J. & Papaconstantinou, Xenophon A., 1988. "Analysis of the stationary Ek/C2/s queueing system," European Journal of Operational Research, Elsevier, vol. 37(2), pages 272-287, November.
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    Cited by:

    1. Seok Ho Chang & Dae Won Choi, 2006. "Modeling and Performance Analysis of a Finite-Buffer Queue with Batch Arrivals, Batch Services, and Setup Times: The M X /G Y /1/K + B Queue with Setup Times," INFORMS Journal on Computing, INFORMS, vol. 18(2), pages 218-228, May.

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