Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 2, Pages 185-204
doi:10.1155/S1048953396000184
Queueing system with passive servers
Byelorussian State University, Department of Applied Mathematics, Minsk, Belarus
Received 1 January 1995; Revised 1 January 1996
Copyright © 1996 Alexander N. Dudin and Valentina I. Klimenok. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper the authors introduce systems in which customers are served by
one active server and a group of passive servers. The calculation of response time
for such systems is rendered by analyzing a special kind of queueing system in a
synchronized random environment. For an embedded Markov chain, sufficient
conditions for the existence of a stationary distribution are proved. A formula
for the corresponding vector generating function is obtained. It is a matrix analog of the Pollaczek-Khinchin formula and is simultaneously a matrix functional
equation. A method for solving this equation is proposed.