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The single server queue in discrete time‐numerical analysis II

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  • Eugene M. Klimko
  • Marcel F. Neuts

Abstract

This paper deals with the numerical problems arising in the computation of higher order moments of the busy period for certain classical queues of the M|G|I type, both in discrete and in continuous time The classical functional equation for the moment generating function of the busy period is used. The higher order derivatives at zero of the moment generating function are computed by repeated use of the classical differentiation formula of Fá di Bruno. Moments of order up to fifty may be computed in this manner A variety of computational aspects of Fá di Bruno's formula, which may be of use in other areas of application, are also discussed in detail.

Suggested Citation

  • Eugene M. Klimko & Marcel F. Neuts, 1973. "The single server queue in discrete time‐numerical analysis II," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(2), pages 305-319, June.
    • Handle: RePEc:wly:navlog:v:20:y:1973:i:2:p:305-319
    DOI: 10.1002/nav.3800200211
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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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