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Infinite-server queueing tandem with Markovian arrival process and service depending on its state

Author

Listed:
  • Alexander Moiseev

    (Tomsk State University)

  • Maria Shklennik

    (Tomsk State University)

  • Evgeny Polin

    (Tomsk State University)

Abstract

We consider the infinite-server queueing tandem with the Markovian arrival process. The service time of requests at the first stage and the probability of their transition to the second stage are determined by the type of request that corresponds to the state of the arrival process at the time when the request arrived. A study of this system was performed under an asymptotic condition of a high rate of arrivals. A Gaussian approximation is obtained for the joint stationary probability distribution of the number of requests at the stages of the system under the condition. Based on this approximation, the problem of computing the optimal number of servers for specific values of model parameters is solved. Further, the obtained asymptotic result is extended to the case when a service at the second stage also depends on the request type, as well as on the case of systems with the number of stages greater than two.

Suggested Citation

  • Alexander Moiseev & Maria Shklennik & Evgeny Polin, 2023. "Infinite-server queueing tandem with Markovian arrival process and service depending on its state," Annals of Operations Research, Springer, vol. 326(1), pages 261-279, July.
    • Handle: RePEc:spr:annopr:v:326:y:2023:i:1:d:10.1007_s10479-023-05318-1
    DOI: 10.1007/s10479-023-05318-1
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    References listed on IDEAS

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    1. Yonit Barron & David Perry & Wolfgang Stadje, 2016. "A make-to-stock production/inventory model with MAP arrivals and phase-type demands," Annals of Operations Research, Springer, vol. 241(1), pages 373-409, June.
    2. H. M. Jansen & M. R. H. Mandjes & K. De Turck & S. Wittevrongel, 2016. "A large deviations principle for infinite-server queues in a random environment," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 199-235, February.
    3. A. Krishnamoorthy & S. Jaya & B. Lakshmy, 2015. "Queues with interruption in random environment," Annals of Operations Research, Springer, vol. 233(1), pages 201-219, October.
    4. Anastasia Winkler, 2013. "Dynamic scheduling of a single-server two-class queue with constant retrial policy," Annals of Operations Research, Springer, vol. 202(1), pages 197-210, January.
    5. H. Zhang, 1999. "A multi‐class cyclic arrival queue with a single server," Annals of Operations Research, Springer, vol. 87(0), pages 333-350, April.
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    Cited by:

    1. Sindhu S & Achyutha Krishnamoorthy & Dmitry Kozyrev, 2023. "A Two-Server Queue with Interdependence between Arrival and Service Processes," Mathematics, MDPI, vol. 11(22), pages 1-25, November.

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