Multi-server queueing system with reserve servers

Authors

Keywords:

queuing system, reserve servers, batch Markovian arrival process, phase type distribution, stationary distribution, performance characteristics
Supporting Agencies
This work has been financially supported by the joint grant of Belarusian Republican Foundation for Fundamental Research (No. Ф18Р-136) and Russian Foundation for Fundamental Research (No. 18-57-00002).

Abstract

In this paper, we investigate a multi-server queueing system with an unlimited buffer, which can be used in the design of energy consumption schemes and as a mathematical model of unreliable real stochastic systems. Customers arrive to the system in a batch Markovian arrival process, the service times are distributed according to the phase law. If the service time of the customer by the server exceeds a certain random value distributed according to the phase law, this server receives assistance from the reserve server from a finite set of reserve servers. In the paper, we calculate the stationary distribution and performance characteristics of the system.

Author Biography

  • Valentina I. Klimenok, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    doctor of science (physics and mathematics), full professor; chief researcher at the laboratory of applied probabilistic analysis, faculty of applied mathematics and computer science

References

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Published

2019-11-28

Issue

No. 3 (2019): Journal of the Belarusian State University. Mathematics and Informatics

Section

Probability Theory and Mathematical Statistics

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How to Cite

[1]
Klimenok, V.I. 2019. Multi-server queueing system with reserve servers. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Nov. 2019), 57–70. DOI:https://doi.org/10.33581/2520-6508-2019-3-57-70.