Wiener-Hopf analysis of an M/G/1 queue with negative customers and of a related class of random walks

N. Bayer, O.J. Boxma

    Research output: Contribution to journalArticleAcademicpeer-review

    29 Citations (Scopus)

    Abstract

    Two variants of an M/G/1 queue with negative customers lead to the study of a random walkX n+1=[X n + \mathbbE(sXn )E(sXn) , corresponding to a representation of the data which is suitable for the queueing model. Alternative representations and derivations are discussed. With this formula, we calculate the queue length generating function of an M/G/1 queue with negative customers, in which the negative customers can remove ordinary customers only at the end of a service. If the service is exponential, the arbitrarytime queue length distribution is a mixture of two geometrical distributions.
    Original languageEnglish
    Pages (from-to)301-316
    Number of pages16
    JournalQueueing Systems: Theory and Applications
    Volume23
    Issue number1-4
    DOIs
    Publication statusPublished - 1996

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