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arXiv · 0908.4585

Stability of a spatial polling system with greedy myopic service

Lasse Leskelä·Falk Unger
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Abstract

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 range. 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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Lasse Leskelä, Falk Unger. 2010-04-27. Stability of a spatial polling system with greedy myopic service. https://doi.org/10.1007/s10479-010-0762-6

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