非乘积解随机Petri网的乘积形式近似求解

Product Form Approximate Solution for No Product Form Solution Stochastic Petri Nets

讨论了非乘积解随机 Petri网的近似求解问题 .将 Marie方法引入到随机 Petri网的近似分析中 ,利用随机 Petri网中已有的结论将该方法中的分解原则推广到更一般的情形 ,使其应用范围更广 .利用运算分析法对这些分解原则作了形式化描述 ,在此基础上 ,给出了有关结论的数学证明 .最后 ,对这种近似方法作了误差分析 ,找出了产生误差的原因 。

This paper discusses the approximate solution of no-product-form solution SPNs. One possible approximate method is product-form approximation solution for no-product-form solution SPNs. The product-form approximation techniques are successfully used in Queueing Networks (QNs), such as Marie's method. The idea of Marie's method is to replace a subsystem by an equivalent exponential service station with load-dependent service rates. In this case, the parameters of the equivalent server are obtained by analyzing the subsystem in isolation under a load-dependent arrival process. The inter arrival time is assumed to be exponentially distributed with rate λ (n), where n is the total number of customers currently presented in the network. The load-dependent service rates are then set equal to the so-called conditional throughput of the subsystem in isolation. Since the parameters λ (n) are unknown, an iterative procedure must be used to calculate them. Marie mainly applied his technique to the case of closed queueing networks with general service times. In that case, each subsystem consists of a single station which is analyzed in isolation as a λ (n)/GI/1/N queue. We introduce Marie's method to SPNs. We first extend the decomposition principles in Marie's method to more general cases by using the results in SPNs and thus this technique can be applied to more cases. We formally describe these principles by using operational analysis. Based on the formal description we provide mathematical proofs of the results in Marie's method. Finally, we give a justification of his method's accuracy by analyzing the sources of errors.