Queueing system with passive servers

Alexander N. Dudin and Valentina I. Klimenok

International Journal of Stochastic Analysis, 1996, vol. 9, 1-20

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.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:417476

DOI: 10.1155/S1048953396000184

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