Stability of a spatial polling system with greedy myopic service
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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.
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- Stability of a spatial polling system with greedy myopic service
Annals of Operations Research
Volume 198, Issue 1 , pp 165-183
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- Spatial queueing system
- Dynamic traveling repairman
- Quadratic Lyapunov functional
- Spatial–temporal point process
- Spatial birth-and-death process
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