| Article ID: | iaor19962274 |
| Country: | United States |
| Volume: | 9 |
| Issue: | 2 |
| Start Page Number: | 185 |
| End Page Number: | 204 |
| Publication Date: | Apr 1996 |
| Journal: | Journal of Applied Mathematics and Stochastic Analysis |
| Authors: | Dudin Alexander N., Klimenok Valentina I. |
| Keywords: | markov processes |
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.