Stability of a spatial polling system with greedy myopic service

Lasse Leskelä () and Falk Unger ()

Annals of Operations Research, 2012, vol. 198, issue 1, 165-183

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 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. Copyright Springer Science+Business Media, LLC 2012

Keywords: Spatial queueing system; Dynamic traveling repairman; Quadratic Lyapunov functional; Spatial–temporal point process; Spatial birth-and-death process (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10479-010-0762-6

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