Queueing system with passive servers. (1996)

• Record Type: Journal Article
• Authors: Dudin, Alexander N.; Klimenok, Valentina I.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 9:Number 2(1996)
• Page Start: 185
• Page End: 204
• Publication Date: 1996
• Subjects: queueing system -- synchronized random environment (SRE) -- two-dimensional embedded Markov chain -- linear matrix functional equation; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953396000184
• Languages: English
• ISSNs: 1048-9533

Abstract

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.