Spatial Queueing Systems

This chapter describes a spatial queueing model for stochastic service systems in which customers or units move about and receive services in a region or a general space. The state of such a system is a point process on a space that evolves over time as a “measure-valued” Markov jump process. Each unit moves in the space according to a Markovian routing mechanism and it receives services at the locations it visits. The service times are exponentially distributed and the rates, as in a queueing system, depend on the congestion or configuration of the points in the system. The types of dependencies are extensions of those in Jackson and Whittle queueing networks.