Stability of a spatial polling system with greedy myopic service

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 unchang...

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Bibliographic Details
Published in:arXiv.org 2010-04
Main Authors: Leskelä, Lasse, Unger, Falk
Format: Article
Language:English
Subjects:
Computer simulation
Customers
Mathematical models
Neighborhoods
Polling schemes
Queues
Queuing theory
Stability
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0908.4585