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

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

8 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

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AU - Mathieu, Fabien

AU - Norros, Ilkka

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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.

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KW - infinite particle system

KW - palm probability

KW - coupling from the past

KW - moment measure

KW - repulsion

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Mutual service processes in Euclidean spaces: existence and ergodicity

Abstract

Keywords

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