Closed Exponential Networks of Queues with Saturation: The Jackson-Type Stationary Distribution and Its Asymptotic Analysis
Closed Exponential Networks of Queues with Saturation: The Jackson-Type Stationary Distribution and Its Asymptotic Analysis
复制标题
饱和队列的闭指数网络：Jackson型平稳分布及其渐近分析
DOI：
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发表时间：
1979
影响因子：
1.7
通讯作者：
B. Pittel
中科院分区：
文献类型：
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作者：
B. Pittel
提出了两种具有饱和的闭合排队网络模型。假设第一个模型满足“可逆性”条件，则这两个模型的平稳分布都是乘积形式的。具有有限服务能力所产生的容许状态空间的排队网络是一般方案的最重要的特殊变种。给出了平稳分布在大客户情况下的渐近分析，表明要获得极限分布的参数，必须解决一个特殊的非线性规划问题。特别地，对于容量有限的服务，饱和概率通过对应的队列大小的线性限制的对偶的拉格朗日乘子来渐近表示。
Two models of a closed queueing network with saturation are proposed. Given that the “reversibility” condition holds in the first model, the stationary distribution is shown to be of product-form for either of them. Queueing networks with the space of admissible states generated by limited capacities of servers is the most important special variant of the general scheme. The asymptotic analysis of the stationary distribution in the case of a large number of customers is given and shows that a special nonlinear programming problem must be solved to obtain parameters of the limiting distribution. In particular, saturation probabilities are asymptotically expressed through the Lagrangian multipliers dual to corresponding linear restrictions of queue-sizes for servers with limited capacities.