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Optimal Open-Loop Routing and Threshold-Based Allocation in TWO Parallel QUEUEING Systems with Heterogeneous Servers

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  • Dmitry Efrosinin

    (Institute for Stochastics, Johannes Kepler University Linz, 4040 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 17, V.A. Trapeznikov Institute of Control Sciences of RAS, 117997 Moscow, Russia)

Abstract

In this paper, we study the problem of optimal routing for the pair of two-server heterogeneous queues operating in parallel and subsequent optimal allocation of customers between the servers in each queue. Heterogeneity implies different servers in terms of speed of service. An open-loop control assumes the static resource allocation when a router has no information about the state of the system. We discuss here the algorithm to calculate the optimal routing policy based on specially constructed Markov-modulated Poisson processes. As an alternative static policy, we consider an optimal Bernoulli splitting which prescribes the optimal allocation probabilities. Then, we show that the optimal allocation policy between the servers within each queue is of threshold type with threshold levels depending on the queue length and phase of an arrival process. This dependence can be neglected by using a heuristic threshold policy. A number of illustrative examples show interesting properties of the systems operating under the introduced policies and their performance characteristics.

Suggested Citation

  • Dmitry Efrosinin & Natalia Stepanova, 2021. "Optimal Open-Loop Routing and Threshold-Based Allocation in TWO Parallel QUEUEING Systems with Heterogeneous Servers," Mathematics, MDPI, vol. 9(21), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2766-:d:669254
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    References listed on IDEAS

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    1. Linn I. Sennott, 1989. "Average Cost Optimal Stationary Policies in Infinite State Markov Decision Processes with Unbounded Costs," Operations Research, INFORMS, vol. 37(4), pages 626-633, August.
    2. Delasay, Mohammad & Kolfal, Bora & Ingolfsson, Armann, 2012. "Maximizing throughput in finite-source parallel queue systems," European Journal of Operational Research, Elsevier, vol. 217(3), pages 554-559.
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