Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 2, Pages 185-204
doi:10.1155/S1048953396000184
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.