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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 2004-11
上傳時間 24-Dec-2008 13:30:18 (UTC+8)
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
dc.creator (作者) Xiuli Chaoen_US
dc.creator (作者) 陸行zh_TW
dc.date (日期) 2004-11en_US
dc.date.accessioned 24-Dec-2008 13:30:18 (UTC+8)-
dc.date.available 24-Dec-2008 13:30:18 (UTC+8)-
dc.date.issued (上傳時間) 24-Dec-2008 13:30:18 (UTC+8)-
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/18705-
dc.description.abstract (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.en_US
dc.format application/en_US
dc.language enen_US
dc.language en-USen_US
dc.language.iso en_US-
dc.relation (關聯) Queueing Systems: Theory and Applications, 48(3/4), 399-419en_US
dc.subject (關鍵詞) heterogeneous queues;monotonicity;blocking probability;stochastic directional convexit;increasing convex orderingen_US
dc.title (題名) A Stochastic Directional Convexity Result and Its Application in Comparison of Queuesen_US
dc.type (資料類型) articleen
dc.identifier.doi (DOI) 10.1023/B:QUES.0000046583.57857.f1en_US
dc.doi.uri (DOI) http://dx.doi.org/10.1023/B:QUES.0000046583.57857.f1en_US