The methodology of multicriterial assessment of Petri nets’ apparatus

Abstract

This article emphasizes the effectiveness and relevance of the using of the apparatus of Petri nets for modeling of complex computing systems. Due to the fact that the methods of analysis existing in this theory do not allow estimating the resources required to build the desired model of the system, there is a problem of shortage of criteria for its evaluation in terms of the complexity of the construction. In the article we consider the method of analysis of a random Petri net based on the complexity of its building and relationships of internal units - subnets. The purpose of this article is a software implementation of such an assessment within the theory of PN structures. Due to the fact, that structural approach allows to perform the operation of decomposition of the original system, this model can be divided into subnets of minimal dimension, that will allow to make its quantitative assessment - ranking. To determine the total assessment of the input and output data of the system we will perform the analysis of head and tail positions of the net taking into account the weights of the input and output arcs of these positions. In order to identify an extent of the cost required to build the system, the number of operations of union of subnet transitions and positions. These subnets have minimal dimension in the original PN. Thus, the article demonstrates the formal implementation of assessment technique modules with using of algebra of sets, and the rules of splitting the PN structure into elementary blocks are formulated. The example of a comparative assessment of the two Petri nets based on the proposed complexity criteria is given; the plots of PN in different coordinate systems are displayed. The article presents the results of the research - a plot of PN structures in three-dimensional space, implemented using described software. It demonstrates the accuracy of PN assessment by structural analysis in comparing with a non-automated visual one. This approach can be applied for comparative assessment of computer systems in terms of complexity of their construction and size of input and output data.