Optimum Route Sequence Search In Petri Net Based On Reliability And Reparability Of Transition

Since the Petri Net first be proposed by C.A.Petri in his doctoral dissertation in 1962, many researchers extend and improve this theory. People have done many researches about backbone of Petri Net since very earlier. The way which connects the input place and the output place and the total delay is shorter than any other ways is called backbone. It's the most efficient path in Petri Net, and it can determine capability of system in a way. A lot of problem in real life can be described as backbone's search of Petri Net. Transition has time delay in Petri Net; many researches described time delay as the impact factor, which affect the backbone's search of Petri Net. When the conditions are complicated, time delay can't describe the actual question. The article proposes a new Petri Net whose transition has reliability and reparability based on deeply research for backbone's search theory of Petri Net. We must consider not only the impact of time delay but also the impact of reliability and reparability when search for the backbone of Petri Net.This article will research on finding backbone of Petri Net with the clew that transition has reliability and reparability:This article analyzes the reliability of transition whose age obeys Weibull distribution. We build stochastic Petri Net model which has considered reliability and time delay. We combine Petri Net and Ant Colony Algorithm to search for backbone, the article also improves Ant Colony Algorithm in choice strategy, update odor elements and update place elements. Then, the article offers the algorithm of finding backbone, the result of instances proves that the Algorithm is correct.Un-repairable transition only has reliability; repairable transition not only has reliability but also has reparability. The usability, which synthetically considers the reliability and reparability, is another important factor affects backbone's search of Petri Net. The article offers another algorithm of finding backbone based on usability of transition. The algorithm improves Ant Colony Algorithm over again and proposes random search token. This Ant Colony algorithm, which considers usability, time delay and service cost, is used to find the backbone in Petri Net. Result of instances proves that the Algorithm can find the backbone.Distribution functions of reliability and reparability are diversity, they can obey exponential distribution both, and they also can obey different distribution. When reliability obeys Weibull distribution and reparability obey logarithmic normal distribution, it adjoins to real life the most. After get the computation method of usability, the article builds Petri Net model. Using some new methods to modify Ant Colony algorithm, such as choice strategy based on normal distribution, updates method of odor elements based on uniform distribution and odor balance factor, volatile factor modify odor and so on. At last the article uses the improved Ant Colony algorithm to find backbone. Result of instances proves that the Algorithm can find the backbone.After the article searches for backbone three times, the theory combines Ant Colony algorithm and Petri Net is proved completely correct. The article applies this theory on the question of partner's selection in supply chain network, instances proves that algorithm can find the best partners. After all, this article deepens the search theory of backbone's search in Petri Net and enlarges the coverage of backbone's search. People can completely and deeply acquire the research theory and application scenario of backbone's search in Petri Net by this article.