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The Departure Process of the GI / G /1 Queue and Its MacLaurin Series

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  • Jian-Qiang Hu

    (Boston University, Boston, Massachusetts)

Abstract

In this paper, we study the departure process of the GI / G /1 queue. We develop a simple recursive procedure to calculate the MacLaurin series of its moments and covariances with respect to a parameter in the service time. Based on this recursive procedure the explicit formulas of the coefficients of these MacLaurin series can be obtained in terms of derivatives of the probability density function of the interarrival time evaluated at zero and the moments of the interarrival time and the service time. One important application of these MacLaurin series is that they can be used to obtain the entire response curves of the moments and variances of the departure process, for example, via interpolation by polynomials or rational functions.

Suggested Citation

  • Jian-Qiang Hu, 1996. "The Departure Process of the GI / G /1 Queue and Its MacLaurin Series," Operations Research, INFORMS, vol. 44(5), pages 810-815, October.
    • Handle: RePEc:inm:oropre:v:44:y:1996:i:5:p:810-815
    DOI: 10.1287/opre.44.5.810
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    Cited by:

    1. J.P.C. Blanc, 2002. "Computation of Autocorrelations of Interdeparture Times by Numerical Transform Inversion," Annals of Operations Research, Springer, vol. 112(1), pages 83-100, April.
    2. Girish, Muckai K. & Hu, Jian-Qiang, 2000. "Higher order approximations for the single server queue with splitting, merging and feedback," European Journal of Operational Research, Elsevier, vol. 124(3), pages 447-467, August.
    3. Weimin Dai & Jian-Qiang Hu, 2022. "Correlated queues with service times depending on inter-arrival times," Queueing Systems: Theory and Applications, Springer, vol. 100(1), pages 41-60, February.
    4. Girish, Muckai K. & Hu, Jian-Qiang, 2001. "Approximations for the departure process of the G/G/1 queue with Markov-modulated arrivals," European Journal of Operational Research, Elsevier, vol. 134(3), pages 540-556, November.

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