Annals of Operations Research

, Volume 198, Issue 1, pp 165–183

Stability of a spatial polling system with greedy myopic service

Article

DOI: 10.1007/s10479-010-0762-6

Cite this article as:
Leskelä, L. & Unger, F. Ann Oper Res (2012) 198: 165. doi:10.1007/s10479-010-0762-6

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.

Keywords

Spatial queueing systemDynamic traveling repairmanQuadratic Lyapunov functionalSpatial–temporal point processSpatial birth-and-death process

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Aalto UniversityAaltoFinland
  2. 2.UC BerkeleyBerkeleyUSA