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Moment inequalities for the discrete-time bulk service queue

Author

Listed:
  • D. Denteneer
  • A.J.E.M. Janssen
  • J.S.H. van Leeuwaarden

Abstract

For the discrete-time bulk service queueing model, the mean and variance of the steady-state queue length can be expressed in terms of moments of the arrival distribution and series of the zeros of a characteristic equation. In this paper we investigate the behaviour of these series. In particular, we derive bounds on the series, from which bounds on the mean and variance of the queue length follow. We pay considerable attention to the case in which the arrivals follow a Poisson distribution. For this case, additional properties of the series are proved leading to even sharper bounds. The Poisson case serves as a pilot study for a broader range of distributions. Copyright Springer-Verlag 2005

Suggested Citation

  • D. Denteneer & A.J.E.M. Janssen & J.S.H. van Leeuwaarden, 2005. "Moment inequalities for the discrete-time bulk service queue," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(1), pages 85-108, March.
    • Handle: RePEc:spr:mathme:v:61:y:2005:i:1:p:85-108
    DOI: 10.1007/s001860400388
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    Cited by:

    1. Mohan Chaudhry & Veena Goswami, 2022. "The Geo / G a , Y /1/ N Queue Revisited," Mathematics, MDPI, vol. 10(17), pages 1-17, September.
    2. M. S. van den Broek & J. S. H. van Leeuwaarden & I. J. B. F. Adan & O. J. Boxma, 2006. "Bounds and Approximations for the Fixed-Cycle Traffic-Light Queue," Transportation Science, INFORMS, vol. 40(4), pages 484-496, November.

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