International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1996 / Article

Open Access

Volume 9 |Article ID 417476 | 20 pages | https://doi.org/10.1155/S1048953396000184

Queueing system with passive servers

Received01 Jan 1995
Revised01 Jan 1996

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.

Copyright © 1996 Hindawi Publishing Corporation. 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.


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