Stability of Random Admissible-Set Scheduling in Spatially Continuous Wireless Systems

We examine the stability of wireless networks whose users are distributed over a compact space. A subset of users is called {\it admissible} when their simultaneous activity obeys the prevailing interference constraints and, in each time slot, an admissible subset of users is selected uniformly at random to transmit one packet. We show that, under a mild condition, this random admissible-set scheduling mechanism achieves maximum stability in a broad set of scenarios, and in particular in symmetric cases. The proof relies on a description of the system as a measure-valued process and the identification of a Lyapunov function.