On the Steady-State Solution of the M / C 2 ( a, b )/ s Queueing System

Dimitris Bertsimas and Xenophon Papaconstantinou
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Dimitris Bertsimas: Massachusetts Institute of Technology, Cambridge, Massachusetts
Xenophon Papaconstantinou: National Technical University of Athens, Athens, Greece

Transportation Science, 1988, vol. 22, issue 2, 125-138

Abstract: This study solves the bulk queueing system M / C 2 ( a , b )/ s with Poisson arrivals and service time pdf of Coxian-2 type. When a server becomes free a group of customers of size at most b can be served. The server is not allowed to process a group of size less than a , 1 (le) a (le) b . Using the generalized method of stages, an explicit form is found for the probabilities of states with all servers busy and then through a recursive structure the problem is reduced to a linear system of s + 1 equations with s + 1 unknowns. An O ( as 3 ) algorithm is proposed. Closed form expressions for the waiting-time, idle-servers and service-batch distributions are derived.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:22:y:1988:i:2:p:125-138

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