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Open AccessFeature PaperArticle

Optimization of Queueing Model with Server Heating and Cooling

1
Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
2
Applied Mathematics and Comminications Technology Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(9), 768; https://doi.org/10.3390/math7090768
Received: 29 July 2019 / Revised: 17 August 2019 / Accepted: 19 August 2019 / Published: 21 August 2019
(This article belongs to the Special Issue Stochastic Processes: Theory and Applications)
The operation of many real-world systems, e.g., servers of data centers, is accompanied by the heating of a server. Correspondingly, certain cooling mechanisms are used. If the server becomes overheated, it interrupts processing of customers and needs to be cooled. A customer is lost when its service is interrupted. To prevent overheating and reduce the customer loss probability, we suggest temporal termination of service of new customers when the temperature of the server reaches the predefined threshold value. Service is resumed after the temperature drops below another threshold value. The problem of optimal choice of the thresholds (with respect to the chosen economical criterion) is numerically solved under quite general assumptions about the parameters of the system (Markovian arrival process, phase-type distribution of service time, and accounting for customers impatience). Numerical examples are presented. View Full-Text
Keywords: processor heating and cooling; markovian arrival process; phase-type service time distribution; impatience processor heating and cooling; markovian arrival process; phase-type service time distribution; impatience
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Dudina, O.; Dudin, A. Optimization of Queueing Model with Server Heating and Cooling. Mathematics 2019, 7, 768.

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