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A Two-Server Queue with Interdependence between Arrival and Service Processes

Author

Listed:
  • Sindhu S

    (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
    Probability Theory and Cyber Security Department, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198 Moscow, Russia)

Abstract

In this paper, we analyse a queueing system with two servers where the arrival and service processes are interdependent. The evolution of these processes is governed by transitions on the product space of three Markov chains, which are descriptors of the arrival and service processes. The transitions in this Markov chain follow a semi-Markov rule and the exponential distribution governs the sojourn times in the states. The stability condition of the system is derived and the stationary distribution is calculated for the system in equilibrium. Several important performance measures are provided, and numerical illustrations of the model are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4692-:d:1283038
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    References listed on IDEAS

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    8. 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.
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