Finite M/M/1 retrial model with changeable service rate

  • M.S. Bratiichuk Silesian University of Technology Gliwice, Poland
  • A.A. Chechelnitsky Taras Shevchenko National University Kyiv, Ukraine
  • I.Ya. Usar Taras Shevchenko National University Kyiv, Ukraine
Keywords: retrial queueing system; ergodic distribution; service rate

Abstract

The article deals with M/M/1 -type retrial queueing system with finite orbit. It is supposed
that service rate depends on the loading of the system. The explicit formulae for ergodic
distribution of the number of customers in the system are obtained. The theoretical results are
illustrated by numerical examples.

Author Biographies

M.S. Bratiichuk, Silesian University of Technology Gliwice, Poland

Silesian University of Technology
Gliwice, Poland

A.A. Chechelnitsky, Taras Shevchenko National University Kyiv, Ukraine

Taras Shevchenko National University
Kyiv, Ukraine

I.Ya. Usar, Taras Shevchenko National University Kyiv, Ukraine

Taras Shevchenko National University
Kyiv, Ukraine

References

J.R. Artalejo, A. Gomes-Corral, Retrial queueing systems. Computational Approach, Springer-Verlag, 2008.

J.R. Artalejo, Accessible bibliography on retrial queue, Math. Comput. Modell., 30 (1999), 1–6.

G.I. Falin, J.G.C. Templeton, Retrial queues, London Chapman & Hall., 1997.

L. Kosten, Stochastic theory of service systems, Pergamon press, Oxford, 1973.

J. Warland, An introduction to queueing networks, Prentice Hall, 1988.

M.S. Bratiichuk, A.A. Chechelnitsky, I.Ja. Usar, M/M/1 Retrial queueing system with variable service rate, Ukrainian Mathematical Journal, 72 (2020), 403–415.

Z. Xuelu, W. Jinting, M. Qing, Optimal design for a retrial queueing system with state-dependent service rate, Journal of Systems Science and Complexity, 30 (2017), 883–900.

Published
2021-10-23
How to Cite
1.
Bratiichuk M, Chechelnitsky A, Usar I. Finite M/M/1 retrial model with changeable service rate. Mat. Stud. [Internet]. 2021Oct.23 [cited 2022Jan.20];56(1):96-102. Available from: http://www.matstud.org.ua/ojs/index.php/matstud/article/view/217
Section
Articles