Alexander N. Dudin, Valentina I. Klimenok, "Queueing system with passive servers", International Journal of Stochastic Analysis, vol. 9, Article ID 417476, 20 pages, 1996. https://doi.org/10.1155/S1048953396000184
Queueing system with passive servers
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.
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