Mutual service processes in Euclidean spaces: existence and ergodicity

Francois Baccelli, Fabien Mathieu, Ilkka Norros

    Research output: Contribution to journalArticleScientificpeer-review

    3 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 languageEnglish
    Pages (from-to)95-140
    Number of pages46
    JournalQueueing Systems
    Volume86
    Issue number1-2
    DOIs
    Publication statusPublished - 1 Jun 2017
    MoE publication typeA1 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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