Efficient computerized Petri net approach for the enumeration of the sets of path identifiers for reliability analysis of broadcasting networks

Abstract

An efficient Petri net approach for enumerating the sets of path identifiers for the reliability analysis of broadcasting networks is presented. The sets of path identifiers are enumerated with the help of a place-to-transilion incident matrix of the Petri net model of Ihe given network. The reachability, marking and firing concepts of Petri nets are used to give a Petri net interpretation to certain properties of the network. The proposed method is applicable to ST-connectivity, SKT-connectivity and SAT-connectivity problems. The sets of path identifiers are generated in ascending order of cardinality which is one of the basic requirements for efficiency in most of the techniques available for obtaining the symbolic and numerical system reliability expressions. The developed algorithm has been programmed in FOR-TRAN-77 and tested on various types of data. The proposed method directly obtains the sels of path identifiers for SKT- and SAT-connectivity problems without the necessity of generating the ST-minimal path sets. In comparison to the previously published approach, the algorithm is conceptually simpler and requires less computer time and memory space. Examples have been provided to demonstrate the effectiveness of the method. A comparison of CPU time and memory requirement of the present method with an existing method has also been given.