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

Author

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  • Manuel J. Carrillo

    (The Rand Corporation, 1700 Main Street, Santa Monica, California 90401)

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.

Suggested Citation

  • Manuel J. Carrillo, 1991. "Note---Extensions of Palm's Theorem: A Review," Management Science, INFORMS, vol. 37(6), pages 739-744, June.
    • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:6:p:739-744
    DOI: 10.1287/mnsc.37.6.739
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    Cited by:

    1. Gillen, David & Hasheminia, Hamed, 2013. "Estimating the demand responses for different sizes of air passenger groups," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 24-38.
    2. Volovoi, Vitali, 2013. "Universal failure model for multi-unit systems with shared functionality," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 141-149.

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