Algorithmic Analysis of Finite-Source Multi-Server Heterogeneous Queueing Systems

Dmitry Efrosinin, Natalia Stepanova and Janos Sztrik
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Dmitry Efrosinin: Insitute for Stochastics, Johannes Kepler University Linz, Altenbergerstrasse 69, 4040 Linz, Austria
Natalia Stepanova: V.A. Trapeznikov Institute of Control Sciences of RAS, Profsoyuznaya 65, 117997 Moscow, Russia
Janos Sztrik: Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, Egyetem tér 1, 4032 Debrecen, Hungary

Mathematics, 2021, vol. 9, issue 20, 1-24

Abstract: The paper deals with a finite-source queueing system serving one class of customers and consisting of heterogeneous servers with unequal service intensities and of one common queue. The main model has a non-preemptive service when the customer can not change the server during its service time. The optimal allocation problem is formulated as a Markov-decision one. We show numerically that the optimal policy which minimizes the long-run average number of customers in the system has a threshold structure. We derive the matrix expressions for performance measures of the system and compare the main model with alternative simplified queuing systems which are analysed for the arbitrary number of servers. We observe that the preemptive heterogeneous model operating under a threshold policy is a good approximation for the main model by calculating the mean number of customers in the system. Moreover, using the preemptive and non-preemptive queueing models with the faster server first policy the lower and upper bounds are calculated for this mean value.

Keywords: finite-source queueing system; preemptive and non-preemptive service; Markov-decision process; policy-iteration algorithm; performance analysis (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 (1)

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