Stability of a spatial polling system with greedy myopic service

This paper studies a spatial queueing system on a circle, polled at random locations by a myopic server that can only observe customers in a bounded neighborhood. The server operates according to a greedy policy, always serving the nearest customer in its neighborhood, and leaving the system unchanged at polling instants where the neighborhood is empty. This system is modeled as a measure‐valued random process, which is shown to be positive recurrent under a natural stability condition that does not depend on the server’s scan radius. When the interpolling times are light‐tailed, the stable system is shown to be geometrically ergodic. The steady‐state behavior of the system is briefly discussed using numerical simulations and a heuristic light‐traffic approximation.