On the structuring of the involve discrete information of Petri model for acceleration computation of invariants purpose

The present work is devoted to one of the tasks of modern scientific research related to the construction and verification of models that allow to organize and systematize a significant amount of information (Big Data) of real systems for making decisions on development and optimization.

To build an adequate and informative model for systematic analysis of huge volumes, tools of qualitative ordering are needed. At present, the various extensions of Petri nets is actively used to implement these tasks. In this direction, we consider that the joint application of component modeling [5] and the truncated incidence matrix [7] to structure information in the time Petri model of system, based on Big Data, is efficient.

To achieve the stated result, the model for solving problems of this type is constructed in the form of a component time Petri net [11], in which the time characteristic is associated with transitions. This model is a compact-descriptive model with time, structuring information understood by a person, into a system that adequately represents this information in data. To verify the obtained model, in the fundamental equation of the time component Petri net the truncated incidence matrix is used to find its structural invariants (complete invariants of behavior and state). The truncated incidence matrix takes into account the functioning logic of time Petri model and reduces the amount of computation by the number of parallel and synchronized processes. Considering the elements of the incidence matrix as the accumulated discrete information, involved in the process of finding invariants, we can, with a joint application of the truncated incidence matrix and component modeling, obtain the compression ratio of the involved discrete information.

In this paper the computable efficiency of the joint application of the truncated incidence matrix and component modeling is considered using the example of the task of extracting, organizing and using information from three distributed databases. When the task under study is modeled by the component time Petri net, the compression ratio of the involved discrete information is k = 4.2. The ratio k for the detailed time model is 2.5 as the truncated incidence matrix instead of the incidence matrix. As a result of the joint application of the component time model and the truncated incidence matrix we have the 8.3 time decrease in the amount of involved discrete information.