Stability of a spatial polling system with greedy myopic service

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  • Centrum voor Wiskunde en Informatica

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. We also briefly discuss how the stationary mean number of customers behaves in light and heavy traffic.

Details

Original languageEnglish
Pages (from-to)165-183
JournalAnnals of Operations Research
Volume198
Issue number1
Publication statusPublished - 2012
MoE publication typeA1 Journal article-refereed

ID: 6335239