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Robustness of the cμ -Rule for an Unreliable Single-Server Two-Class Queueing System with Constant Retrial Rates

Author

Listed:
  • Dmitry Efrosinin

    (Institute for Stochastics, Johannes Kepler University Linz, 4040 Linz, Austria)

  • Natalia Stepanova

    (Scientific and Production Company “INSET”, Moscow 129085, Russia)

  • Janos Sztrik

    (Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary)

Abstract

We study the robustness of the c μ -rule for the optimal allocation of a resource consisting of one unreliable server to parallel queues with two different classes of customers. The customers in queues can be served with respect to a FIFO retrial discipline, when the customers at the heads of queues repeatedly try to occupy the server at a random time. It is proved that for scheduling problems in the system without arrivals, the c μ -rule minimizes the total average cost. For the system with arrivals, it is difficult directly to prove the optimality of the same policy with explicit relations. We derived for an infinite-buffer model a static control policy that also prescribes the service for certain values of system parameters exclusively for the class- i customers if both of the queues are not empty, with the aim to minimize the average cost per unit of time. It is also shown that in a finite buffer case, the c μ -rule fails.

Suggested Citation

  • Dmitry Efrosinin & Natalia Stepanova & Janos Sztrik, 2023. "Robustness of the cμ -Rule for an Unreliable Single-Server Two-Class Queueing System with Constant Retrial Rates," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:4002-:d:1244284
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    References listed on IDEAS

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    1. Antonis Economou & Spyridoula Kanta, 2011. "Equilibrium customer strategies and social–profit maximization in the single‐server constant retrial queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 107-122, March.
    2. Wang, Jinting & Zhang, Xuelu & Huang, Ping, 2017. "Strategic behavior and social optimization in a constant retrial queue with the N-policy," European Journal of Operational Research, Elsevier, vol. 256(3), pages 841-849.
    3. K. Avrachenkov & E. Morozov & R. Nekrasova & B. Steyaert, 2014. "Stability Analysis And Simulation Of N-Class Retrial System With Constant Retrial Rates And Poisson Inputs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-18.
    4. Dimitriou, Ioannis, 2018. "A two-class queueing system with constant retrial policy and general class dependent service times," European Journal of Operational Research, Elsevier, vol. 270(3), pages 1063-1073.
    5. 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.
    6. Efrosinin, Dmitry & Winkler, Anastasia, 2011. "Queueing system with a constant retrial rate, non-reliable server and threshold-based recovery," European Journal of Operational Research, Elsevier, vol. 210(3), pages 594-605, May.
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