# Mutual Service Processes in Euclidean Spaces: Existence and Ergodicity

3 DYOGENE - Dynamics of Geometric Networks
Inria de Paris, CNRS - Centre National de la Recherche Scientifique : UMR 8548, DI-ENS - Département d'informatique de l'École normale supérieure
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.
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Cited literature [18 references]

https://hal.inria.fr/hal-01535925
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Submitted on : Friday, June 9, 2017 - 5:12:55 PM
Last modification on : Tuesday, September 22, 2020 - 3:52:11 AM
Long-term archiving on: : Sunday, September 10, 2017 - 1:45:40 PM

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### Citation

François Baccelli, Fabien Mathieu, Ilkka Norros. Mutual Service Processes in Euclidean Spaces: Existence and Ergodicity. Queueing Systems, Springer Verlag, 2017, 86 (1-2), pp.95 - 140. ⟨10.1007/s11134-017-9524-3⟩. ⟨hal-01535925⟩

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