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

John F. Reynolds | Zendy

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

Author(s) -

John F. Reynolds

Publication year - 1968

Publication title -

operations research

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.797

H-Index - 140

eISSN - 1526-5463

pISSN - 0030-364X

DOI - 10.1287/opre.16.1.186

Subject(s) - queue , poisson distribution , autocorrelation , bulk queue , limiting , function (biology) , mathematics , computer science , poisson regression , statistics , computer network , mechanical engineering , population , demography , evolutionary biology , sociology , engineering , biology

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.

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