In this paper, we analyze a queueing system characterized by a space-time arrival process of customers served by a countable set of servers. Customers arrive at points in space and the server stations have space-dependent processing rates. The workload is seen as a Radon measure and the server stations can adapt their power allocation to the current workload. We derive the stability region of the queueing system in the usual stationary ergodic framework. The analysis of this stability region gives some counter-intuitive results. Some specific subclasses of policy are also studied. Wireless communications networks is a natural field of application for the model.
