Stability of a spatial polling system with greedy myopic service

Lasse Leskelä, Falk Unger

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

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

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