Space—Time Poisson Models

Abstract

This chapter covers space—time Poisson models for queueing networks, spatial service or storage systems, and particle systems. Such a model describes the collective movement of units or customers in space and time, where the units enter the system according to a Poisson space—time process and then move about independently of each other. Because of these properties, the evolution of the system can be formulated by certain “random transformations” of Poisson point processes in space and time. We characterize these transformations and then use them in a variety of models. An important example is a network with time-dependent Poisson arrival process and infinite-server nodes with general service times.