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Article

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

1
Insitute for Stochastics, Johannes Kepler University Linz, Altenbergerstrasse 69, 4040 Linz, Austria
2
Department of Information Technologies, Faculty of Mathematics and Natural Sciences, Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya 6, 117198 Moscow, Russia
3
V.A. Trapeznikov Institute of Control Sciences of RAS, Profsoyuznaya 65, 117997 Moscow, Russia
4
Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, Egyetem tér 1, 4032 Debrecen, Hungary
*
Author to whom correspondence should be addressed.
Academic Editor: Mark Kelbert
Mathematics 2021, 9(20), 2624; https://doi.org/10.3390/math9202624
Received: 29 September 2021 / Revised: 13 October 2021 / Accepted: 15 October 2021 / Published: 18 October 2021
(This article belongs to the Special Issue Distributed Computer and Communication Networks)
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. View Full-Text
Keywords: finite-source queueing system; preemptive and non-preemptive service; Markov-decision process; policy-iteration algorithm; performance analysis finite-source queueing system; preemptive and non-preemptive service; Markov-decision process; policy-iteration algorithm; performance analysis
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MDPI and ACS Style

Efrosinin, D.; Stepanova, N.; Sztrik, J. Algorithmic Analysis of Finite-Source Multi-Server Heterogeneous Queueing Systems. Mathematics 2021, 9, 2624. https://doi.org/10.3390/math9202624

AMA Style

Efrosinin D, Stepanova N, Sztrik J. Algorithmic Analysis of Finite-Source Multi-Server Heterogeneous Queueing Systems. Mathematics. 2021; 9(20):2624. https://doi.org/10.3390/math9202624

Chicago/Turabian Style

Efrosinin, Dmitry, Natalia Stepanova, and Janos Sztrik. 2021. "Algorithmic Analysis of Finite-Source Multi-Server Heterogeneous Queueing Systems" Mathematics 9, no. 20: 2624. https://doi.org/10.3390/math9202624

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