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https://ah.lib.nccu.edu.tw/handle/140.119/18705
題名: | A Stochastic Directional Convexity Result and Its Application in Comparison of Queues | 作者: | Xiuli Chao 陸行 |
關鍵詞: | heterogeneous queues;monotonicity;blocking probability;stochastic directional convexit;increasing convex ordering | 日期: | Nov-2004 | 上傳時間: | 24-Dec-2008 | 摘要: | 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. | 關聯: | Queueing Systems: Theory and Applications, 48(3/4), 399-419 | 資料類型: | article | DOI: | http://dx.doi.org/10.1023/B:QUES.0000046583.57857.f1 |
Appears in Collections: | 期刊論文 |
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399-419.pdf | 156.93 kB | Adobe PDF2 | View/Open |
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