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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.<\/jats:p>","DOI":"10.3233\/jifs-231137","type":"journal-article","created":{"date-parts":[[2023,5,9]],"date-time":"2023-05-09T21:08:34Z","timestamp":1683666514000},"page":"1131-1139","source":"Crossref","is-referenced-by-count":1,"title":["Performance analysis of Petri net based on moment generating function"],"prefix":"10.1177","volume":"45","author":[{"given":"Xu","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Computer Science and Technology, Tongji University, Shanghai, China"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-231137_ref1","doi-asserted-by":"crossref","unstructured":"Schwarick M. , Rohr C. , Liu F. , Assaf G. , Chodak J. and Heiner M. , Efficient unfolding of coloured Petri nets using interval decision diagrams, In: Janicki R, Sidorova N, Chatain T. (eds) Application and Theory of Petri nets and Concurrency, Petri netS 2020. Lecture Notes in Computer Science, 2020. 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