Note---Extensions of Palm's Theorem: A Review

Manuel J. Carrillo
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Manuel J. Carrillo: The Rand Corporation, 1700 Main Street, Santa Monica, California 90401

Management Science, 1991, vol. 37, issue 6, 739-744

Abstract: This note reviews the transient behavior the M/G/\infty queue with nonhomogeneous Poisson or compound Poisson input and nonstationary service distribution. In the case of nonhomogeneous Poisson input, the number of customers in the queueing system over time turns out to have a Poisson distribution. The generality of the nonhomogeneity/nonstationarity assumptions and the ease of use of the resulting Poisson distribution broaden the area of applications for Poisson models. These results have found use in modeling multi-echelon repair systems in situations where the number of arrivals or number in service has a variance-to-mean ratio of unity (the Poisson case) or greater than unity.

Keywords: M/G/\infty queue; transient behavior; nonhomogeneous Poisson process; compound Poisson process; batch arrivals and service; multi-echelon repair system (search for similar items in EconPapers)
Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:37:y:1991:i:6:p:739-744

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