Open and closed models for networks of queues
Open and closed models for networks of queues
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DOI：
10.1002/j.1538-7305.1984.tb00084.x
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发表时间：
1984-11
期刊：
影响因子：
--
通讯作者：
W. Whitt
中科院分区：
文献类型：
--
作者：
W. Whitt
本文研究了队列网络的开放模型和封闭模型之间的关系。在开放模型中，工作从外部进入网络，在一个或多个服务中心接受服务，然后离开。在封闭模型中，作业既不进入也不离开网络；相反，固定数量的工作在网络内循环。开放模型在分析上更容易处理，但封闭模型通常看起来更现实。因此，本文研究了使用开放模型来近似封闭模型的方法。一种方法是使用具有指定预期均衡群体的开放模型。这种固定总体均值方法对于近似求解大型封闭模型特别有效，其中“大”可能意味着许多节点或许多作业。这些近似的成功部分是由极限定理解释的：在适当的条件下，固定总体均值方法是渐近正确的。在某些情况下，开放模型方法也会产生封闭模型中性能测量的界限。
This paper investigates the relationship between open and closed models for networks of queues. In open models, jobs enter the network from outside, receive service at one or more service centers, and then depart. In closed models, jobs neither enter nor leave the network; instead, a fixed number of jobs circulate within the network. Open models are analytically more tractable, but closed models often seem more realistic. Hence, this paper investigates ways to use open models to approximate closed models. One approach is to use open models with specified expected equilibrium populations. This fixed-population-mean method is especially effective for approximately solving large closed models, where “large” may mean many nodes or many jobs. The success of these approximations is partly explained by limit theorems: Under appropriate conditions, the fixed-population-mean method is asymptotically correct. In some cases the open-model methods also yield bounds for the performance measures in the closed models.