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- Title
Mutual service processes in Euclidean spaces: existence and ergodicity.
- Authors
Baccelli, François; Mathieu, Fabien; Norros, Ilkka
- Abstract
Consider a set of objects, abstracted to points of a spatially stationary point process in $$\mathbb {R}^d$$ , 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.
- Subjects
EUCLIDEAN distance; POINT processes; STATIONARY processes; INTEGRALS; POISSON processes
- Publication
Queueing Systems, 2017, Vol 86, Issue 1/2, p95
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-017-9524-3