Stability of a spatial polling system with greedy myopic service

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Stability of a spatial polling system with greedy myopic service. / Leskelä, Lasse; Unger, Falk.

In: Annals of Operations Research, Vol. 198, No. 1, 2012, p. 165-183.

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@article{f2dfc208399a414395ebceeb1f766514,
title = "Stability of a spatial polling system with greedy myopic service",
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.",
author = "Lasse Leskel{\"a} and Falk Unger",
year = "2012",
doi = "10.1007/s10479-010-0762-6",
language = "English",
volume = "198",
pages = "165--183",
journal = "Annals of Operations Research",
issn = "0254-5330",
publisher = "Springer Netherlands",
number = "1",

}

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TY - JOUR

T1 - Stability of a spatial polling system with greedy myopic service

AU - Leskelä, Lasse

AU - Unger, Falk

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

U2 - 10.1007/s10479-010-0762-6

DO - 10.1007/s10479-010-0762-6

M3 - Article

VL - 198

SP - 165

EP - 183

JO - Annals of Operations Research

JF - Annals of Operations Research

SN - 0254-5330

IS - 1

ER -

ID: 6335239