## 2 Related Works  
Models based on Petri nets have been used to describe discrete-event systems with the parallel-serial nature of the processes. The reason for choosing PNs is that, unlike traditional models for modeling discrete events (DEs), the PN model provides an intuitive graphical representation of the studied complex system, and has been proven to be more flexible and efficient [7; 8; 9]. Among the many practical applications of Petri nets, works related to the modeling of flexible manufacturing systems (FMSs) stand out. Early work has shown the effectiveness of various Petri nets for simulating production systems for defect and failure prediction [10; 11; 12]. In the subsequent period, new modeling tools for studies of production systems were built, which describe the process of equipment degradation and deterioration [13; 14]. In [12; 15], high-level Petri nets were developed, corresponding to the hierarchical organization of production structures. This explains the continuing interest of researchers, which has led to the creation of various extensions of Petri nets. As a result, the most widely used models are colored CPNs [16; 17], timed TCPNs [18; 19], and stochastic SCPNs [20]. Another relevant area of Petri net model application is in developing, testing, and verifying software systems, computational processes, and communication protocols. Mainly, the successful application of Petri nets should be noted in the description of information processing, microprocessor systems, and others. In such systems, there are strict requirements for fault tolerance and timing relationships. [PERSON] et al. [21; 22] applied CPNs to formalize component operation scheduling, and presented a method for analyzing system dependencies based on a service-oriented architecture (SOA). The various types of dependency relationship are formalized using service algebra. Such a model-driven approach provides a process for reworking and restructuring the software application. [PERSON] and [PERSON] [23] developed a similar approach for requirements analysis in real-time systems. They proposed a reachability-based algorithm for real-time testing of discrete systems, in which timed computational tree logic is used as a specification language, and timed transition graphs are introduced to represent system behavior. Among a wide range of topics for the practical use of PNs, one should highlight the construction of stochastic Petri nets for studying the degradation, aging, and deterioration processes of various units, mechanisms, and machines. The study of these phenomena and processes is necessary for the organization of maintenance and repair. A review of the existing research in this area shows that many researchers successfully use the apparatus of Petri nets to design reliable and maintainable industrial systems in various areas of technology. Preventive and predictive maintenance strategies are used in technological processes; however, discrepancies exist between the mathematical models used and the actual maintenance activities. One of the main reasons for this is insufficient mathematical modeling methods to accurately describe the equipment interactions during maintenance. In this regard, the use of simulation models on Petri nets is actively developing. The relevance of modeling the interactions between units and component manufacturing processes causes the active development of Petri nets in this area. [PERSON] et al. [PERSON] et al. (2019) developed color PNs as a formalization of the temporal aspects of the elements functioning in a decentralized task distribution. Simultaneously, the presentation of the object as a multi-agent system is combined with the CPN model simulation. The CPN model for production-logistics problems, which implements the self-adaptive collaboration method, was investigated by [PERSON] et al. in [PERSON] et al. (2018). The objective of the proposed TCPN model is to minimize the waiting time of all jobs, the makespan, and the electricity consumption of all machines and AGVs.