Reversed processes, product forms and a non-product form☆
Reversed processes, product forms and a non-product form☆
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DOI：
10.1016/j.laa.2004.02.020
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发表时间：
2004-07
影响因子：
1.1
通讯作者：
P. Harrison
中科院分区：
文献类型：
--
作者：
P. Harrison
利用相互作用的马尔可夫过程中各分量的相互作用的反向过程，逐层求出相互作用的马尔可夫过程的平衡联合状态概率。从一个相反的过程中，直接得到联合状态概率的乘积形式解。该方法采用马尔可夫过程代数形式，推广了最近的反向复合代理定理（RCAT）来求解多种类型的并发系统。该类包括具有共享、独占资源的进程、具有Coxian服务时间的后到先服务（LCFS）队列的面向客户的规范以及具有非产品形式解决方案的扩展PS队列。根据这些结果，一个新的，非常简短的BCMP定理证明随之而来。该方法的主要优点是其机械化和象征性实施的潜力。事实上，许多非标准的产品形式已经直接从组合方法中出现。
The equilibrium joint state probabilities of interacting Markov processes are obtained in a hierarchical way, by finding the reversed process of the interaction in terms of the reversed processes of its components. From a reversed process, a product-form solution for the joint state probabilities follows directly. The method uses a Markovian process algebra formalism and generalises the recent Reversed Compound Agent Theorem (RCAT) to solve a diverse class of concurrent systems. This class includes processes with shared, exclusive resources, a customer-oriented specification of a last-come-first-served (LCFS) queue with Coxian service times and an extended PS queue with a non-product form solution. From these results, a new, very short proof of the BCMP theorem ensues. The principal advantage of the methodology is its potential for mechanisation and symbolic implementation. Indeed, many non-standard product-forms have emerged directly from the compositional approach.