Networks of infinite-server queues with nonstationary Poisson input (Q1801811)

This paper deals with a network of infinite-server queues with nonhomogeneous Poisson arrival processes. A unified framework for constructing stochastic processes of interest is provided by stochastically integrating various functionals of the location process with respect to the Poisson arrival process. For Markov routing among the queues, the aggregate arrival rates are obtained as the solution to a system of input equations. Linear ordinary differential equations characterize the time-dependent means and covariances in the totally Markovian case.