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Moments of first passage times in general birth–death processes

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  • Oualid Jouini
  • Yves Dallery

Abstract

We consider ordinary and conditional first passage times in a general birth–death process. Under existence conditions, we derive closed-form expressions for the kth order moment of the defined random variables, k ≥ 1. We also give an explicit condition for a birth–death process to be ergodic degree 3. Based on the obtained results, we analyze some applications for Markovian queueing systems. In particular, we compute for some non-standard Markovian queues, the moments of the busy period duration, the busy cycle duration, and the state-dependent waiting time in queue. Copyright Springer-Verlag 2008

Suggested Citation

  • Oualid Jouini & Yves Dallery, 2008. "Moments of first passage times in general birth–death processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 49-76, August.
    • Handle: RePEc:spr:mathme:v:68:y:2008:i:1:p:49-76
    DOI: 10.1007/s00186-007-0174-9
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    References listed on IDEAS

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    1. Ward Whitt, 1999. "Predicting Queueing Delays," Management Science, INFORMS, vol. 45(6), pages 870-888, June.
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    Cited by:

    1. Giorno, Virginia & Nobile, Amelia G., 2022. "On some integral equations for the evaluation of first-passage-time densities of time-inhomogeneous birth-death processes," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    2. Gontis, V. & Kononovicius, A., 2020. "Bessel-like birth–death process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. Oualid Jouini & Zeynep Akşin & Yves Dallery, 2011. "Call Centers with Delay Information: Models and Insights," Manufacturing & Service Operations Management, INFORMS, vol. 13(4), pages 534-548, October.

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