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Journal Articles Queueing Systems Year : 2017

## Mutual Service Processes in Euclidean Spaces: Existence and Ergodicity

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François Baccelli
Fabien Mathieu
Ilkka Norros
• Function : Author

#### 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.

### Dates and versions

hal-01535925 , version 1 (09-06-2017)

### Licence

Attribution - CC BY 4.0

### Identifiers

• HAL Id : hal-01535925 , version 1
• DOI :

### Cite

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

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