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.
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⟩
