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Analysis of a Queuing System with Possibility of Waiting Customers Jockeying between Two Groups of Servers

Author

Listed:
  • Sergei A. Dudin

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus)

  • Olga S. Dudina

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus)

  • Olga I. Kostyukova

    (Institute of Mathematics, National Academy of Sciences of Belarus, 220072 Minsk, Belarus)

Abstract

In this paper, we consider a queueing system consisting of two multi-server subsystems that is designed for the service of clients arriving at a system according to a Markovian arrival process ( MAP ). Arriving clients receive information about the number of clients present in both subsystems and use this information to make a randomized decision to balk (depart without receiving service) or join the system. In the latter case, they also decide which subsystem they would like to join. One subsystem has an infinite buffer, while the buffer of the second subsystem is finite. The service time distribution is exponential in the first subsystem and phase-type in the second subsystem. During the waiting in the chosen buffers, after the random time intervals, each waiting client checks the status of the alternative subsystem. If some server in that subsystem is idle during this epoch, the client immediately leaves the buffer where it has been staying and starts a service in the alternative subsystem. The problem of computing the steady-state distribution of this system is solved. The feasibility of the proposed solution and certain features of the system’s behavior are numerically illustrated.

Suggested Citation

  • Sergei A. Dudin & Olga S. Dudina & Olga I. Kostyukova, 2023. "Analysis of a Queuing System with Possibility of Waiting Customers Jockeying between Two Groups of Servers," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1475-:d:1100398
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    References listed on IDEAS

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    1. R. L. Disney & W. E. Mitchell, 1970. "A solution for queues with instantaneous jockeying and other customer selection rules," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 17(3), pages 315-325, September.
    2. Kao, Edward P. C. & Lin, Chiunsin, 1990. "A matrix-geometric solution of the jockeying problem," European Journal of Operational Research, Elsevier, vol. 44(1), pages 67-74, January.
    3. Che Kim & Vilena Mushko & Alexander Dudin, 2012. "Computation of the steady state distribution for multi-server retrial queues with phase type service process," Annals of Operations Research, Springer, vol. 201(1), pages 307-323, December.
    4. Yiqiang Zhao & Winfried K. Grassmann, 1995. "Queueing Analysis of a Jockeying Model," Operations Research, INFORMS, vol. 43(3), pages 520-529, June.
    5. Ernest Koenigsberg, 1966. "On Jockeying in Queues," Management Science, INFORMS, vol. 12(5), pages 412-436, January.
    6. Yiqiang Zhao & W. K. Grassmann, 1990. "The shortest queue model with jockeying," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 773-787, October.
    7. Elsayed, E. A. & Bastani, A., 1985. "General solutions of the jockeying problem," European Journal of Operational Research, Elsevier, vol. 22(3), pages 387-396, December.
    8. Dudin, A.N. & Dudin, S.A. & Dudina, O.S. & Samouylov, K.E., 2018. "Analysis of queueing model with processor sharing discipline and customers impatience," Operations Research Perspectives, Elsevier, vol. 5(C), pages 245-255.
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    1. Setareh Boshrouei Shargh & Mostafa Zandieh & Ashkan Ayough & Farbod Farhadi, 2024. "Scheduling in services: a review and bibliometric analysis," Operations Management Research, Springer, vol. 17(2), pages 754-783, June.

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