The Infinite-Server Queue with Poisson Arrivals and Semi-Markovian Services

Marcel F. Neuts and Shun-Zer Chen
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Marcel F. Neuts: Purdue University, Lafayette, Indiana
Shun-Zer Chen: Voorhees College, Denmark, South Carolina

Operations Research, 1972, vol. 20, issue 2, 425-433

Abstract: This paper considers the queue with an infinite number of servers with a Poisson arrival process and with semi-Markovian service times. It studies jointly the queue-length process and the type of the first customer to join the queue after t and obtains transient and asymptotic results that are matrix extensions of the corresponding results of the M / G /∞ queue. In particular, it proves that the limiting distribution of the queue-length process is Poisson.

Date: 1972
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:20:y:1972:i:2:p:425-433

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