关于Petri网中同步距离定义的研究

Discussion on the definition of synchronic distance in Petri net

同步距离是描述2个事件间同步的一个重要的恒定性质,反映了2个变迁之间的独立程度。它对系统的设计、分析和优化提供了很大的帮助。文章研究了Petri网中的同步距离的定义,通过实例分析指出原有定义适用于含有有向回路的网系统。随后将原有定义细化,引入公平性、亚公平性、T-跨来定义新的同步距离。新定义将处于非公平关系的变迁根据亚公平关系分2类情况考虑;对于处于公平关系的变迁根据T-跨分3种情况,讨论了同步距离的求解,并通过实例解决了原有定义存在的问题。

Synchronic distance is an important constant nature to describe the synchronicity between two events and reflects the degree of independence between two transitions.It is very helpful in the design,analysis and optimization of the systems.In this paper,the definition of synchronic distance in Petri net is discussed and it is pointed out that the original definition is mainly fit for net systems with directed circuit by analyzing examples.A new definition about synchronic distance is then presented by introducing fairness,meta-fair relation,and T-bestride in the original definition.The transitions in non-fariness and fairness relations are discussed,and two cases are considered for the meta-fair relation and three cases for the T-bestride relation.Then details about the solution of the synchronic distance are discussed.Finally examples are given which show that the problems in the original definition are solved by the new definition.