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The single server queue in discrete time‐numerical analysis III

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  • Marcel F. Neuts
  • Eugene Klimko

Abstract

This paper deals with the stationary analysis of the finite, single server queue in discrete time. The following stntionary distributions and other quantities of practical interest are investigated: (1) the joint density of the queue length and the residual service time, (2) the queue length distribution and its mean, (3) the distribution of the residual service time and its mean, (4) the distribution and the expected value of the number of customers lost per unit of time due to saturation of the waiting capacity, (5) the distribution and the mean of the waiting time, (6) the asymptotic distribution of the queue length following departures The latter distribution is particularly noteworthy, in view of the substantial difference which exists, in general, between the distributions of the queue lengths at arbitrary points of time and those immediately following departures.

Suggested Citation

  • Marcel F. Neuts & Eugene Klimko, 1973. "The single server queue in discrete time‐numerical analysis III," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(3), pages 557-567, September.
    • Handle: RePEc:wly:navlog:v:20:y:1973:i:3:p:557-567
    DOI: 10.1002/nav.3800200315
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    Cited by:

    1. M.L. Chaudhry & U.C. Gupta, 2003. "Analysis of a finite‐buffer bulk‐service queue with discrete‐Markovian arrival process: D‐MAP/Ga,b/1/N," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(4), pages 345-363, June.
    2. Pianykh, Oleg S. & Perez, Sebastian & Zhang, Chengzhao “Richard”, 2024. "Discrete scheduling and critical utilization," European Journal of Operational Research, Elsevier, vol. 312(2), pages 445-455.
    3. Hugo P. Simão & Warren B. Powell, 1988. "Waiting time distributions for transient bulk queues with general vehicle dispatching strategies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(2), pages 285-306, April.

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