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Stability of a spatial polling system with greedy myopic service

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  • Lasse Leskelä
  • Falk Unger

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

Suggested Citation

  • Lasse Leskelä & Falk Unger, 2012. "Stability of a spatial polling system with greedy myopic service," Annals of Operations Research, Springer, vol. 198(1), pages 165-183, September.
    • Handle: RePEc:spr:annopr:v:198:y:2012:i:1:p:165-183:10.1007/s10479-010-0762-6
    DOI: 10.1007/s10479-010-0762-6
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    References listed on IDEAS

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    1. Ferrari, Pablo A. & Fernández, Roberto & Garcia, Nancy L., 2002. "Perfect simulation for interacting point processes, loss networks and Ising models," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 63-88, November.
    2. Dirk P. Kroese & Volker Schmidt, 1996. "Light-Traffic Analysis for Queues with Spatially Distributed Arrivals," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 135-157, February.
    3. Robert, Philippe, 2010. "The evolution of a spatial stochastic network," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1342-1363, July.
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    Cited by:

    1. Sergey Foss, 2018. "Comments on: Polling: past, present and perspective," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 374-378, October.
    2. Vladimir Vishnevsky & Olga Semenova, 2021. "Polling Systems and Their Application to Telecommunication Networks," Mathematics, MDPI, vol. 9(2), pages 1-30, January.

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