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.