State-dependent Coupling of Quasireversible Nodes
State-dependent Coupling of Quasireversible Nodes
复制标题
准可逆节点的状态相关耦合
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
P. Taylor
中科院分区：
文献类型：
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作者：
W. Henderson;P. Taylor
杰克逊的开创性论文开始了一系列关于乘积型平稳分布网络的研究，这些研究一直持续到今天。紧跟着早期的结果，紧接着是一系列的论文，讨论了乘积形式的平稳分布和网络节点的拟可逆性之间的关系。最近，准可逆性的定义和节点间的耦合机制被扩展到一些后来的产品形式的包含负顾客、信号和批量移动的排队网络。与此同时，一些特殊的排队网络可以具有依赖于网络状态的到达和服务参数，而不仅仅是节点状态，在本文中，我们开始提供一个替代的证明的产品形式的结果Chao和Miyazawa，然后建立在这个证明通过假设一个状态依赖耦合机制的准可逆网络。我们的主要定理是所得网络具有广义乘积形式的平稳分布。最后，我们总结了一些例子的文件。
The seminal paper of Jackson began a chain of research on queueing networks with product-form stationary distributions which continues strongly to this day. Hard on the heels of the early results on queueing networks followed a series of papers which discussed the relationship between product-form stationary distributions and the quasireversibility of network nodes. More recently, the definition of quasireversibility and the coupling mechanism between nodes have been extended so that they apply to some of the later product-form queueing networks incorporating negative customers, signals, and batch movements.In parallel with this research, it has been shown that some special queueing networks can have arrival and service parameters which depend upon the network state, rather than just the node state, and still retain a generalised product-form stationary distribution.In this paper we begin by offering an alternative proof of a product-form result of Chao and Miyazawa and then build on this proof by postulating a state-dependent coupling mechanism for a quasireversible network. Our main theorem is that the resultant network has a generalised product form stationary distribution. We conclude the paper with some examples.