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On Queues with Working Vacation and Interdependence in Arrival and Service Processes

Author

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  • S Sindhu

    (Department of Mathematics, Model Engineering College, Ernakulam 682021, India
    Department of Mathematics, Cochin University of Science and Technology, Ernakulam 682022, India)

  • Achyutha Krishnamoorthy

    (Centre for Research in Mathematics, CMS College, Kottayam 686001, India
    Department of Mathematics, Central University of Kerala, Kasargod 671316, India)

  • Dmitry Kozyrev

    (V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Street, 117997 Moscow, Russia
    Applied Probability and Informatics Department, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia)

Abstract

In this paper, we consider two queuing models. Model 1 considers a single-server working vacation queuing system with interdependent arrival and service processes. The arrival and service processes evolve by transitions on the product space of two Markovian chains. The transitions in the two Markov chains in the product space are governed by a semi-Markov rule, with sojourn times in states governed by the exponential distribution. In contrast, in the second model, we consider independent arrival and service processes following phase-type distributions with representation ( α , T ) of order m and ( β , S ) of order n, respectively. The service time during normal working is the above indicated phase-type distribution whereas that during working vacation is a phase-type distribution with representation ( β , θ S ) , 0 < θ < 1 . The duration of the latter is exponentially distributed. The latter model is already present in the literature and will be briefly described. The main objective is to make a theoretical comparison between the two. Numerical illustrations for the first model are provided.

Suggested Citation

  • S Sindhu & Achyutha Krishnamoorthy & Dmitry Kozyrev, 2023. "On Queues with Working Vacation and Interdependence in Arrival and Service Processes," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2280-:d:1146260
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    References listed on IDEAS

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    1. Boxma, O. J. & Perry, D., 2001. "A queueing model with dependence between service and interarrival times," European Journal of Operational Research, Elsevier, vol. 128(3), pages 611-624, February.
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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.
    2. Gabi Hanukov & Uri Yechiali, 2024. "Orbit while in service," Operational Research, Springer, vol. 24(2), pages 1-32, June.

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