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

Marcel F. Neuts, Shun-Zer Chen

Open publisher page 11 citations

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.

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What this paper is about

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.

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Fork–join queue, Bulk queue, Burke's theorem, Computer science, Queue, Poisson distribution, Markovian arrival process, Multilevel queue

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