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Estimation of the Optimal Threshold Policy in a Queue with Heterogeneous Servers Using a Heuristic Solution and Artificial Neural Networks

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  • Dmitry Efrosinin

    (Insitute for Stochastics, Johannes Kepler University Linz, 4030 Linz, Austria
    Department of Information Technologies, Faculty of Mathematics and Natural Sciences, Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia)

  • Natalia Stepanova

    (Laboratory N17, Trapeznikov Institute of Control Sciences of RAS, 117997 Moscow, Russia)

Abstract

This paper deals with heterogeneous queues where servers differ not only in service rates but also in operating costs. The classical optimisation problem in queueing systems with heterogeneous servers consists in the optimal allocation of customers between the servers with the aim to minimise the long-run average costs of the system per unit of time. As it is known, under some assumptions the optimal allocation policy for this system is of threshold type, i.e., the policy depends on the queue length and the state of faster servers. The optimal thresholds can be calculated using a Markov decision process by implementing the policy-iteration algorithm. This algorithm may have certain limitations on obtaining a result for the entire range of system parameter values. However, the available data sets for evaluated optimal threshold levels and values of system parameters can be used to provide estimations for optimal thresholds through artificial neural networks. The obtained results are accompanied by a simple heuristic solution. Numerical examples illustrate the quality of estimations.

Suggested Citation

  • Dmitry Efrosinin & Natalia Stepanova, 2021. "Estimation of the Optimal Threshold Policy in a Queue with Heterogeneous Servers Using a Heuristic Solution and Artificial Neural Networks," Mathematics, MDPI, vol. 9(11), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1267-:d:566655
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    References listed on IDEAS

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    1. Thomas B. Crabill & Donald Gross & Michael J. Magazine, 1977. "A Classified Bibliography of Research on Optimal Design and Control of Queues," Operations Research, INFORMS, vol. 25(2), pages 219-232, April.
    2. Efrosinin, Dmitry & Sztrik, Janos, 2018. "An algorithmic approach to analysing the reliability of a controllable unreliable queue with two heterogeneous servers," European Journal of Operational Research, Elsevier, vol. 271(3), pages 934-952.
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    Cited by:

    1. Gorbunova, A.V. & Lebedev, A.V., 2023. "Nonlinear approximation of characteristics of a fork–join queueing system with Pareto service as a model of parallel structure of data processing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 409-428.
    2. Opher Baron & Dmitry Krass & Arik Senderovich & Eliran Sherzer, 2024. "Supervised ML for Solving the GI / GI /1 Queue," INFORMS Journal on Computing, INFORMS, vol. 36(3), pages 766-786, May.

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