一种随机Petri网性能等价化简与分析方法

other, and obey the exponential distributionthe of the parameters λ1 ， λ2 ,…, λn respectively, that is to say that the average time of the n varied times are 1/λ1， 1/λ2， …， 1/λn，the delay time of the equivalent time variation is 1/λ.The equation is shown as follows:
华中科技大学 研究生课程考试答题本
考 生 姓 名 张钰彪 考 生 学 号 D201577685
系 、 年 级 计算机系统结构 类 别 非定向博士 考 试 科 目 计算机系统分析与性能评价 考 试 日 期 2015 年 11 月 16 日
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2. SPN four basic structure and the time performance equivalent reduction analysis
Here we assumes that you have mastered basic knowledge of the SPN, go here, shut details please refer to the literature on SPN[8]. Being order, concurrency, choice and cycleStochastic Petri Net in four of the most basic structure, including all SPN models.In this paper, the Stochastic Petri net time performance equivalent reduction,and the basic idea is: make every basic structure as a subnet, with a respectively equivalent to represent the time change, the time changes and the original subnet is equalto time expect to get a simplified SPN model, then the model and the original model have the same time performance.In front of the works[9], given sequential and concurrent model time performance equivalent formula derivation, the only to do is that the conclusion supplement for the selection and circulation model is derived its time performance equivalence formulain detail.
1.Introduction
As Stochastic Petri Net[1] is proposed since 1981(Stochastic Petri Net,called SPN), its theory and analysis technology has gained greately used as a powerful tool for analysis of discrete event dynamic system in computer Network[2], resource sharing system[3] and parallel and concurrent computing research[4] domains. But the SPN model of state space explosion problem greatly limits its analysis ability to large and complexSystem model, so the research of performance equivalent reductionmodel technologyhas always been one of the major problems for the study of stochastic Petri net [5,6]. The structures of stochastic Petri net are diverse, but, concurrency, selection and sequencecircular structures arethe four most common basic structures of a stochastic Petri net, by thisfour basic structures and their mutual nesting,we can derive a class of random.Petri net –elementary stochastic Petri net (ESPN), If you don't consider changing the implementation of the rate, and only from the perspective of the structure of network. ESPN is Free Choice nets (Free ChoiceA subset of the set ). Many systems of SPN model itself or some of these subnets are ESPN. Therefore, the performance of the ESPN equivalent reduction will help to solve the SPN.The
problem of state space explosion, and other reduction technology provide a necessary basis.ESPN has the characteristics of hierarchy, and can be applied to the bottom-up hierarchical analysis. Four basic structure of the basic principle of time performance equivalent reduction and performance equivalent, and type is deduced and proved based on these formulas, puts forward the ESPN's time performance, etc.Price reduction algorithms, the complexity of the algorithm that grows along with the model and the linear growth, is a kind of effective stochastic petri net and a performance analysis method. In order to make the method applicable to more general,the SPN model of performance analysis, a kind of thought is through certain transformation rules, the and compoundhybrid of basic structure into four basic structure and its combination, and such general SPN model can be expressed with ESPN model, which can be performance, etc. This article discusses two kinds of basic structure to the transformation of the basic structure of the rules.
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A method to stochastic Petri net performance equivalent reduction and analysis
Abstract:Stochastic Petri Net(SPN)are a powerful modeling and analyzing tool for system performance evaluation.But theproblem of state space's explosion of SPNlimits its ability to analyze complex and large-scale systems.So itismore feasible to simplify SPNmodel on the basis of performance equivalence before analyzing it.In this paper,the authors define a class of SPN-ElementarySPN(ESPN)which is composed of four elementary subnets including sequence subnet,parallel subnet,choice subnet and iterationsubnet,and propose a group of performance equivalence formulas for the four elementary subnets,as well as a method of performanceequivalence simplification and analysis for ESPN with linear time complexity.In addition,two transforming rules are put forward totransform non-elementary subnets into combined elementary subnets such that the proposed algorithm can be used in analysis of moregeneral SPN. Key words:stochastic Petri nets;elementary stochastic Petri nets;performance equivalence;performance analysis