Note—Extensions of Palm's Theorem: A Review
综述了M/G/∞排队系统在非齐次泊松或复合泊松输入及非平稳服务分布下的瞬态行为，指出顾客数服从泊松分布，并讨论了这些结果在多级维修系统建模中的应用。
This note reviews the transient behavior the M/G/∞ 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.