Extensions of Palm's Theorem: A Review
RAND CORP SANTA MONICA CA
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This note reviews the transient behavior the MGinfinity queue with nonhomogeneous Poisson or compound Poisson and nonstationary service distribution. In the case of nonhomogeneous Poisson input, the number of customers in the queueing system over turns out to have a Poisson distributions. The generality of the nonhomogeneitynonstationarity 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.
- Operations Research