Mutual service processes in Euclidean spaces: existence and ergodicity

Francois Baccelli; Fabien Mathieu; Ilkka Norros

doi:10.1007/s11134-017-9524-3

Mutual service processes in Euclidean spaces: existence and ergodicity

Francois Baccelli
, Fabien Mathieu
, Ilkka Norros

Nokia Oyj
The University of Texas at Dallas

Research output: Contribution to journal › Article › Scientific › peer-review

9 Citations (Scopus)

Abstract

Consider a set of objects, abstracted to points of a spatially stationary point process in R^d, that deliver to each other a service at a rate depending on their distance. Assume that the points arrive as a Poisson process and leave when their service requirements have been fulfilled. We show how such a process can be constructed and establish its ergodicity under fairly general conditions. We also establish a hierarchy of integral balance relations between the factorial moment measures and show that the time-stationary process exhibits a repulsivity property.

Original language	English
Pages (from-to)	95-140
Journal	Queueing Systems
Volume	86
Issue number	1-2
DOIs	https://doi.org/10.1007/s11134-017-9524-3
Publication status	Published - 1 Jun 2017
MoE publication type	A1 Journal article-refereed

Keywords

spatial birth and death process
infinite particle system
palm probability
coupling from the past
moment measure
repulsion

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10.1007/s11134-017-9524-3

Cite this

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abstract = "Consider a set of objects, abstracted to points of a spatially stationary point process in Rd, that deliver to each other a service at a rate depending on their distance. Assume that the points arrive as a Poisson process and leave when their service requirements have been fulfilled. We show how such a process can be constructed and establish its ergodicity under fairly general conditions. We also establish a hierarchy of integral balance relations between the factorial moment measures and show that the time-stationary process exhibits a repulsivity property.",

keywords = "spatial birth and death process, infinite particle system, palm probability, coupling from the past, moment measure, repulsion",

author = "Francois Baccelli and Fabien Mathieu and Ilkka Norros",

note = "Funding Information: The authors thank Mayank Manjrekar and the two reviewers for their comments on the paper. The research of the first author was supported by an award from the Simons Foundation (\# 197982 to The University of Texas at Austin). The work of the third author was supported by the Academy of Finland with Senior Researcher funding and by EIT ICT Labs through the project DCDWN. The work presented in this paper has been partly carried out at LINCS (http://www.lincs.fr ). Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media New York. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

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AU - Baccelli, Francois

AU - Mathieu, Fabien

AU - Norros, Ilkka

N1 - Funding Information: The authors thank Mayank Manjrekar and the two reviewers for their comments on the paper. The research of the first author was supported by an award from the Simons Foundation (# 197982 to The University of Texas at Austin). The work of the third author was supported by the Academy of Finland with Senior Researcher funding and by EIT ICT Labs through the project DCDWN. The work presented in this paper has been partly carried out at LINCS (http://www.lincs.fr ). Publisher Copyright: © 2017, Springer Science+Business Media New York. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

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Y1 - 2017/6/1

N2 - Consider a set of objects, abstracted to points of a spatially stationary point process in Rd, that deliver to each other a service at a rate depending on their distance. Assume that the points arrive as a Poisson process and leave when their service requirements have been fulfilled. We show how such a process can be constructed and establish its ergodicity under fairly general conditions. We also establish a hierarchy of integral balance relations between the factorial moment measures and show that the time-stationary process exhibits a repulsivity property.

AB - Consider a set of objects, abstracted to points of a spatially stationary point process in Rd, that deliver to each other a service at a rate depending on their distance. Assume that the points arrive as a Poisson process and leave when their service requirements have been fulfilled. We show how such a process can be constructed and establish its ergodicity under fairly general conditions. We also establish a hierarchy of integral balance relations between the factorial moment measures and show that the time-stationary process exhibits a repulsivity property.

KW - spatial birth and death process

KW - infinite particle system

KW - palm probability

KW - coupling from the past

KW - moment measure

KW - repulsion

UR - https://www.scopus.com/pages/publications/85018801059

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SP - 95

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JO - Queueing Systems

JF - Queueing Systems

IS - 1-2

ER -

Mutual service processes in Euclidean spaces: existence and ergodicity

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Keywords

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