Separable equilibrium state probabilities via time reversal in Markovian process algebra
Separable equilibrium state probabilities via time reversal in Markovian process algebra
复制标题
马尔可夫过程代数中时间反转的可分离平衡状态概率
DOI：
10.1016/j.tcs.2005.08.007
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Ting Ting Lee
中科院分区：
文献类型：
--
作者：
P. Harrison;Ting Ting Lee
反向复合代理定理（RCAT）是一个合成结果，它使用马尔可夫过程代数（MPA）来推导两个连续时间马尔可夫链之间的某些相互作用的反向过程。从这个反向过程，与给定的，向前的过程，联合状态概率可以表示为一个产品的形式，虽然没有一般的算法已经给出。本文首先将RCAT推广到多个（两个以上）合作代理，从而消除了在任意数量的进程的合作中对多个应用程序和归纳证明的需要。一个新的结果显示了一个简单的随机等价合作，同步过程和相应的并行，异步过程。这大大简化了新的多代理定理的证明，该定理包括所需乘积形式解本身作为并行组件中给定状态概率的乘积的陈述。由此导出的逆过程和乘积形式依赖于某些速率方程的解，并且首次表明，在温和的条件下存在唯一的解--当然是对于扩散网络和G-网络。
The reversed compound agent theorem (RCAT) is a compositional result that uses Markovian process algebra (MPA) to derive the reversed process of certain interactions between two continuous time Markov chains at equilibrium. From this reversed process, together with the given, forward process, the joint state probabilities can be expressed as a product-form, although no general algorithm has previously been given. This paper first generalises RCAT to multiple (more than two) cooperating agents, which removes the need for multiple applications and inductive proofs in cooperations of an arbitrary number of processes. A new result shows a simple stochastic equivalence between cooperating, synchronised processes and corresponding parallel, asynchronous processes. This greatly simplifies the proof of the new, multi-agent theorem, which includes a statement of the desired product-form solution itself as a product of given state probabilities in the parallel components. The reversed process and product-form thus derived rely on a solution to certain rate equations and it is shown, for the first time, that a unique solution exists under mild conditions—certainly for queueing networks and G-networks.