Research of a retrial queueing system with exclusion of customers and three-phase phased by follow-up

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Abstract

In this paper, we consider a retrial queueing system (RQ-system) which receives to the input a Poisson flow with a given intensity. If at the time of customer the server is busy, the displacement of customer standing on the server takes place. Customers that do not have time to be successfully serviced go into orbit, in order to, after an accidental exponential delay, again turn to the server for maintenance. It is shown that the limiting characteristic function of the number of customers in the orbit and the states of the server converges to a three-dimensional Gaussian distribution. The mean vector and covariance matrix are obtained for this distribution. A stationary probability distribution of the server states is also found.

About the authors

Anatolii Andreevich Nazarov

Tomsk State University

Email: anazarov@fpmk.tsu.ru
Doctor of technical sciences, Professor

Yana Evgenevna Izmailova

Tomsk State University

Candidate of physico-mathematical sciences, no status

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