Mutual service processes in Euclidean spaces: existence and ergodicity

Francois Baccelli, Fabien Mathieu, Ilkka Norros

    Research output: Contribution to journalArticleScientificpeer-review

    1 Citation (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

    Fingerprint

    Ergodicity
    Service process
    Integral
    Stationary process
    Poisson process
    Point process

    Keywords

    • spatial birth and death process
    • infinite particle system
    • palm probability
    • coupling from the past
    • moment measure
    • repulsion

    Cite this

    Baccelli, Francois ; Mathieu, Fabien ; Norros, Ilkka. / Mutual service processes in Euclidean spaces: existence and ergodicity. In: Queueing Systems. 2017 ; Vol. 86, No. 1-2. pp. 95-140.
    @article{dcc2825018504b7b9765159e53c03f45,
    title = "Mutual service processes in Euclidean spaces: existence and ergodicity",
    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.",
    keywords = "spatial birth and death process, infinite particle system, palm probability, coupling from the past, moment measure, repulsion",
    author = "Francois Baccelli and Fabien Mathieu and Ilkka Norros",
    year = "2017",
    month = "6",
    day = "1",
    doi = "10.1007/s11134-017-9524-3",
    language = "English",
    volume = "86",
    pages = "95--140",
    journal = "Queueing Systems",
    issn = "0257-0130",
    publisher = "Springer",
    number = "1-2",

    }

    Mutual service processes in Euclidean spaces: existence and ergodicity. / Baccelli, Francois; Mathieu, Fabien; Norros, Ilkka.

    In: Queueing Systems, Vol. 86, No. 1-2, 01.06.2017, p. 95-140.

    Research output: Contribution to journalArticleScientificpeer-review

    TY - JOUR

    T1 - Mutual service processes in Euclidean spaces: existence and ergodicity

    AU - Baccelli, Francois

    AU - Mathieu, Fabien

    AU - Norros, Ilkka

    PY - 2017/6/1

    Y1 - 2017/6/1

    N2 - 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.

    AB - 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.

    KW - spatial birth and death process

    KW - infinite particle system

    KW - palm probability

    KW - coupling from the past

    KW - moment measure

    KW - repulsion

    UR - http://www.scopus.com/inward/record.url?scp=85018801059&partnerID=8YFLogxK

    U2 - 10.1007/s11134-017-9524-3

    DO - 10.1007/s11134-017-9524-3

    M3 - Article

    VL - 86

    SP - 95

    EP - 140

    JO - Queueing Systems

    JF - Queueing Systems

    SN - 0257-0130

    IS - 1-2

    ER -