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    National Tsing Hua University Institutional Repository > 電機資訊學院 > 電機工程學系 > 期刊論文 >  Perturbation analysis of the M/M/1 queue in a Marko- vian Environment via the matrix-geometric method


    Please use this identifier to cite or link to this item: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/72585


    Title: Perturbation analysis of the M/M/1 queue in a Marko- vian Environment via the matrix-geometric method
    Authors: Cheng-Shang Chang;Randolph D. Nelson
    教師: 張正尚
    Date: 1993
    Publisher: Taylor & Francis
    Relation: Stochastic Models, Taylor & Francis, Volume 9, Issue 2, 1993, Pages 233-246
    Keywords: time dependent queues
    perturbation analysis
    matrix-geometric method
    Ross's conjecture
    Abstract: In this paper, we consider a family of M(t)/M/1 queues in which customers arrive according to nonhomogenous Poisson processes with intensity We assume that λt(ε) is an irreducible finite-state Markov process. Based on the matrix-geometric method, we use perturbation analysis to obtain the second order approximations for the expected queue length for two cases where ε is small and where ε is large. Using these approximations, we show that the expected waiting times are strictly decreasing in ε when ε is small. In the case where ε is large, we show that the expected waiting times are strictly decreasing in ε if the intensity process is dynamically reversible. These results partially answer a question posed by Rolski
    Relation Link: http://www.tandf.co.uk/journals/default.asp
    URI: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/72585
    Appears in Collections:[電機工程學系] 期刊論文

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