Fluid queue driven by an M/M/1 queue

Jorma Virtamo, Ilkka Norros

    Research output: Contribution to journalArticleScientificpeer-review

    49 Citations (Scopus)

    Abstract

    A fluid queue receiving its input from the output of a preceding M/M/1 queue is considered. The input can be characterized as a Markov modulated rate process and the well known spectral decomposition technique can be applied. The novel features in this system relate to the nature of the spectrum, which is shown to be composed of a continuous part and one or two discrete points depending on whether the load of the fluid queue is less or greater than the output to input rate ratio. Explicit expressions of the generalized eigenvectors are given in terms of Chebyshev polynomials of the second kind, and the resolution of unity is determined. The solution for the buffer content distribution is obtained as a simple integral expression. Numerical examples are given.
    Original languageEnglish
    Pages (from-to)373-386
    Number of pages14
    JournalQueueing Systems
    Volume16
    Issue number3-4
    DOIs
    Publication statusPublished - 1994
    MoE publication typeA1 Journal article-refereed

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