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A Queuing-Type Birth-and-Death Process Defined on a Continuous-Time Markov Chain

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  • Uri Yechiali

    (Tel-Aviv University, Tel Aviv, Israel)

Abstract

This paper considers an n -phase generalization of the typical M / M /1 queuing model, where the queuing-type birth-and-death process is defined on a continuous-time n -state Marker chain. It shows that many models analyzed in the literature can be considered special cases of this framework. The paper focuses on the steady-state regime, and observes that, in general, closed-form results for the limiting probabilities are difficult to obtain, if at all possible. Hence, numerical methods should be employed. For an interesting special case, explicit results are obtained that are analogous to the classical solutions for the simple M / M /1 queue.

Suggested Citation

  • Uri Yechiali, 1973. "A Queuing-Type Birth-and-Death Process Defined on a Continuous-Time Markov Chain," Operations Research, INFORMS, vol. 21(2), pages 604-609, April.
    • Handle: RePEc:inm:oropre:v:21:y:1973:i:2:p:604-609
    DOI: 10.1287/opre.21.2.604
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    Cited by:

    1. Jan-Pieter Dorsman & Kristen Gardner, 2024. "New directions in pass-and-swap queues," Queueing Systems: Theory and Applications, Springer, vol. 107(3), pages 205-256, September.
    2. Jung Baek & Ho Lee & Se Lee & Soohan Ahn, 2008. "A factorization property for BMAP/G/1 vacation queues under variable service speed," Annals of Operations Research, Springer, vol. 160(1), pages 19-29, April.
    3. Mayorga, Maria E. & Ahn, Hyun-Soo, 2011. "Joint management of capacity and inventory in make-to-stock production systems with multi-class demand," European Journal of Operational Research, Elsevier, vol. 212(2), pages 312-324, July.
    4. Guodong Pang & Andrey Sarantsev & Yana Belopolskaya & Yuri Suhov, 2020. "Stationary distributions and convergence for M/M/1 queues in interactive random environment," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 357-392, April.

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