An introduction to spatial queues

The aim of this article is to introduce the methodology of random measures into the theory of spatial queues. By the latter, the paper means queueing systems where each customer’s location in space is taken into account explicitly. After a few preliminaries, it shall illustrate the uses of random measures on some M/G/• type queues and on an M/G/1 queue system where a single server goes from one customer to the next depending on the configuration of customers present in the space. As the paper shall point out, a large number of priority queueing systems and networks of queues with different classes of customers are subsumed and extended by these models. On the other hand, the results it shall obtain in the last section (with moving server) are somewhat incomplete and should be regarded as the start of a research program.