Product forms for queueing networks with state-dependent multiple job transitions
Product forms for queueing networks with state-dependent multiple job transitions
复制标题
具有状态相关的多个作业转换的排队网络的产品形式
DOI：
--
复制
发表时间：
1991
影响因子：
1.2
通讯作者：
N. van Dijk
中科院分区：
文献类型：
--
作者：
R. Boucherie;N. van Dijk
一个一般框架的连续时间排队网络的研究与同时状态相关的服务完成，如由于并发服务或离散时间开槽和状态相关的批处理路由，如最典型的建模阻塞。利用群局部平衡的重要概念，给出了平稳分布为乘积型的充要条件。这些条件和建设性的计算产品的形式是基于仅仅是局部解决方案的组局部平衡方程，通常可以解决明确的具体网络。此外，分解定理，提出了分离的服务和路由条件。一般批量服务和批量路由的例子产生的产品形式，在此结束。通过各种例子说明，已知的结果离散和连续时间的网络是统一和扩展。
A general framework of continuous-time queueing networks is studied with simultaneous state dependent service completions such as due to concurrent servicing or discrete-time slotting and with state dependent batch routings such as most typically modelling blocking. By using a key notion of group-local-balance, necessary and sufficient conditions are given for the stationary distribution to be of product form. These conditions and a constructive computation of the product form are based upon merely local solutions of the group-local-balance equations which can usually be solved explicitly for concrete networks. Moreover, a decomposition theorem is presented to separate service and routing conditions. General batch service and batch routing examples yielding a product form are hereby concluded. As illustrated by various examples, known results on both discrete- and continuous-time queueing networks are unified and extended.