正态分布随机Petri网的串并行结构化简

Reducing the Series-Parallel Structure of the Normal Generalized Stochastic Petri Nets

基于正态分布随机Petri网的串行和并行两种基本结构的化简开展研究,推导出在正态分布广义随机Petri网中化简串行模型的等价理论公式,即合成执行时间为各个变迁的执行时间之和,仍服从正态分布,并且合成均值等于所有变迁执行时间的均值之和,合成标准偏差等于所有变迁执行时间标准偏差的方和根。还提出了并行模型的模拟仿真计算方法,分析了两个并行变迁独立不同分布时的情况,并给出了近似估算公式,在公式中,均值较大的变迁权重较大。

This paper adopts a novel approach to reduction techniques of serial and parallel connection models in the normal generalized stochastic Petri net （NGSPN）. The equivalent theorems of reducing the NGSPN＇s serial connection model is deduced. An availability method for reducing the parallel connection model is proposed and emulated. We also present an asymptotic formula for reducing the two parallel transitions connection model under independent and non-identically distributed cases. The proposed theorems and methods are especially useful in modeling and analyzing complex and large scale systems with Petri net.