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

Dmitry Efrosinin and Natalia Stepanova
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Dmitry Efrosinin: Insitute for Stochastics, Johannes Kepler University Linz, 4030 Linz, Austria
Natalia Stepanova: Laboratory N17, Trapeznikov Institute of Control Sciences of RAS, 117997 Moscow, Russia

Mathematics, 2021, vol. 9, issue 11, 1-14

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.

Keywords: heterogeneous servers; policy-iteration algorithm; heuristic solution; artificial neural networks (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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