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.
KeywordsStationary Distribution Invariant Measure Poisson Process Service Rate Sojourn Time
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