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Letter to the Editor—Some Results for the Bulk-Arrival Infinite-Server Poisson Queue

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  • John F. Reynolds

    (University College of South Wales and Monmouthshire, U.K.)

Abstract

An infinite server queue is considered in which an arrival is actually a group (of random size) of customers. A generating function for the time-dependent queue length is obtained, and used to show that the limiting distribution is compound Poisson. It is also shown that the regression of queue length at time t on the initial length is linear, and from this an expression for the autocorrelation function is deduced.

Suggested Citation

  • John F. Reynolds, 1968. "Letter to the Editor—Some Results for the Bulk-Arrival Infinite-Server Poisson Queue," Operations Research, INFORMS, vol. 16(1), pages 186-189, February.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:1:p:186-189
    DOI: 10.1287/opre.16.1.186
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