Performance analysis of Petri net based on moment generating function

The Petri net structure of workflow is used to model, and the moment generating function is used to analyze the time performance of workflow, and the complexity of analysis is given. It provides basic theory and basis for analysis and verification. The calculation of time complexity is given for sequence, concurrency, cycle, conflict (selection) and mutual exclusion. The performance analysis method based on moment generating function can be used to analyze the performance of arbitrarily distributed bounded or unbounded random Petri nets. Establish a broad-random Petri net model that conforms to the concept of workflow. Then, based on statistical analysis and experience estimation of relevant data in the actual system, analyze the time nature of the on-demand service based on the analysis method based on behavioral expression, and obtain some valuable performance and index information. A necessary and sufficient condition for maintaining reliability of a workflow network model is given; A polynomial decomposition algorithm for P-invariants is proposed; Combining the moment function, a performance analysis method for workflow systems is established. An example is given to verify the effectiveness of the algorithm.