Multi-server queueing system with reserve servers

Authors

DOI:

https://doi.org/10.33581/2520-6508-2019-3-57-70

Keywords:

queuing system, reserve servers, batch Markovian arrival process, phase type distribution, stationary distribution, performance characteristics

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.