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    政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 >  Item 140.119/18705
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/18705

    Title: A Stochastic Directional Convexity Result and Its Application in Comparison of Queues
    Authors: Xiuli Chao
    Keywords: heterogeneous queues;monotonicity;blocking probability;stochastic directional convexit;increasing convex ordering
    Date: 2004-11
    Issue Date: 2008-12-24 13:30:18 (UTC+8)
    Abstract: Second order properties of queues are important in design and analysis of service systems. In this paper we show that the blocking probability of M/M/C/N queue is increasing directionally convex in (λ,−μ), where λ is arrival rate and μ is service rate. To illustrate the usefulness of this result we consider a heterogeneous queueing system with non-stationary arrival and service processes. The arrival and service rates alternate between two levels (λ1,μ1) and (λ2,μ2), spending an exponentially distributed amount of time with rate cα i in level i, i=1,2. When the system is in state i, the arrival rate is λ i and the service rate is μ i . Applying the increasing directional convexity result we show that the blocking probability is decreasing in c, extending a result of Fond and Ross [7] for the case C=N=1.
    Relation: Queueing Systems: Theory and Applications, 48(3/4), 399-419
    Data Type: article
    DOI 連結: http://dx.doi.org/10.1023/B:QUES.0000046583.57857.f1
    DOI: 10.1023/B:QUES.0000046583.57857.f1
    Appears in Collections:[應用數學系] 期刊論文

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