# A Petri Net Approach for Business Process Modeling and Simulation
## 8 Conclusions  
This research work has presented several key contributions in the field of BP modeling using PNs. The following results were achieved:  
1. Development of a BP modeling algorithm. The algorithm utilizes PNs to schematize and represent business processes, providing a structured approach for modeling and analyzing the flow of activities within an organization. 2. Description of basic structures of Petri nets. This study introduces the concept of basic structures, which can help in defining the arrangement of places, transitions, and arcs in a Petri net representation of business processes. These structures facilitate the understanding and analysis of process flows. 3. Software platform development. A software platform was created to demonstrate the functionality of the algorithm. The platform allows users to register the activities of a business process, visualize the Petri net graph, simulate the movement of tokens, and analyze the behavior of the process through mathematical representations derived from simulation data. 4. Compared to ProM and Disco, the application proposed in this document has a flatter learning curve, as the concepts handled are reduced to the following:  
Figure 21: Mathematical representation of the PN for Process 2. Figure 22: Comparison between Process 1 and Process 2. * Record the time of a sample that occupies the activities related to a process (1) in any database or spreadsheet with an objective \(X\) and determine its probability distribution (Appendix A). Simulate process (1) in the proposed application. * Record the time of a sample that occupies the activities related to a process (2) in any database or spreadsheet with the same objective \(X\) and determine its probability distribution (Appendix A). Simulate process (2) in the proposed application. * After the respective simulations have been executed, compare the times of the simulations for processes (1) and (2) in order to determine which is better. * Notably, it is not necessary to capture the times of the activities or import them into the application's database. The only activity necessary is to indicate the type of probability distribution and its necessary parameters. * Performance measurement and comparison. The simulation capabilities of the software platform enable the measurement of performance for different business processes. By analyzing factors such as execution time and selecting the appropriate probability distribution, the platform provides insights into process efficiency and effectiveness. Furthermore, the mathematical representations of business processes allows for direct comparison and identification of better- and worse-performing processes. * Comparison study. A comparison is provided between the Petri nets-based approach to modeling business processes and the generalized nets-based approach. The use of PNs in business process modeling contributes to objective and mathematical analysis, thereby reducing subjectivity. The practical impact of this research work lies in its ability to support organizations in improving their processes by enhancing efficiency, effectiveness, flexibility, cost reduction, quality improvement, and execution times. Conceptualization, [PERSON] and [PERSON]; methodology, [PERSON]-[PERSON], [PERSON], [PERSON], [PERSON] and [PERSON]; software, S.M.-G.; investigation, [PERSON] and [PERSON]; writing-original draft preparation, S.M.-G.; writing--review and editing, [PERSON]-[PERSON], [PERSON], [PERSON] and [PERSON]; project administration, [PERSON]; funding acquisition, [PERSON]. All authors have read and agreed to the published version of the manuscript. This study was supported by the Autonomous University of Hidalgo (UAEH) and the National Council for Humanities, Sciences and Technologies (CONAHCYT) with project number CB-2017-2018-A1-S-43008. [PERSON] was supported by CONAHCYT grant number 1008908. Not applicable. The data presented in this study are available in this paper.