M/M/1 retrial queueing model with variable service rate

  • M. S. Bratiichuk Silez. University of Technology, Poland
  • A. A. Chechelnitsky Kiev National University. Taras Shevchenko
  • I. Ya. Usar Kiev National University. Taras Shevchenko


UDC 519.21<br>

The paper deals with queueing system of the type M/M/1 with repeated claims in the case where the service intensitydepends on the loading of the system, i.e., on the number of claims in the line to be served. We establish the existenceconditions and the formulas for ergodic distribution of the number of claims in the system with bounded and unboundedlines of repeated claims.

Author Biography

M. S. Bratiichuk, Silez. University of Technology, Poland




Artalejo, Jesus R.; Gomez-Corral, Antonio. Retrial queueing systems. A computational approach. Springer-Verlag, Berlin, 2008. xiv+318 pp. ISBN: 978-3-540-78724-2 doi: 10.1007/978-3-540-78725-9

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

Anisimov, Vladimir V.; Artalejo, Jesus R. Analysis of Markov multiserver retrial queues with negative arrivals. Queueing Syst. 39 (2001), no. 2-3, 157--182. doi: 10.1023/A:1012796517394

E. A. Lebedev, I. A. Makushenko, H. V. Livinska, I. Ya. Usar,On steady-state analysis of $[M|M|m|m+n]$ -typeretrial queueing systems, Inform. Technol. and Math. Modelling, Queueing Theory and Appl., Commun. Comput. andInform. Sci., 800, 133 – 146 (2017).

Gross, Donald; Shortle, John F.; Thompson, James M.; Harris, Carl M. Fundamentals of queueing theory. Fourth edition. Wiley Series in Probability and Statistics. John Wiley & Sons, Inc., Hoboken, NJ, 2008. xiv+500 pp. ISBN: 978-0-471-79127-0 doi: 10.1002/9781118625651

Economou, Antonis; Kanta, Spyridoula. Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs. Oper. Res. Lett. 36 (2008), no. 6, 696--699. doi: 10.1016/j.orl.2008.06.006

V. I. Klimenok, Оптимизация динамического управления режимом работы информационно-вычислительныхсистем с повторными вызовами (Russian) Optimizacziya dinamicheskogo upravleniya rezhimom raboty` informaczionno-vy`chislitel`ny`khsistem s povtorny`mi vy`zovami, Avtomatika i vy`chislit. tekhnika, No 1, 25 – 30 (1990).

Zhang, Xuelu; Wang, Jinting; Ma, Qing. Optimal design for a retrial queueing system with state-dependent service rate. J. Syst. Sci. Complex. 30 (2017), no. 4, 883--900. doi: 10.1007/s11424-017-5097-9

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

How to Cite
Bratiichuk, M. S., A. A. Chechelnitsky, and I. Y. Usar. “M/M/1 Retrial Queueing Model With Variable Service Rate”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 3, Mar. 2020, pp. 355-6, doi:10.37863/umzh.v72i3.813.
Research articles