## 2 Related Work
The challenges of edge computing [23], such as system modeling with deterministic time delay, industrial task design, and unloading, real-time container technology, resource management in the heterogeneous computing environment and constrained resource environment, and broader forms of resource sharing are proposed. OT experts believe that it is necessary to master the industrial mechanism model so that AI can be applied a really work on edge; IT experts emphasize the role of AI in building a common computing architecture [24]. Edge intelligence in industries needs to closely combine the AI algorithm and model with industrial knowledge and mechanisms in order to give full play to its effect. The value of the cloud edge combination provides users with cloud-consistent functionality and applications and experiences on infrastructure. Kubedge integrates cloud, management, edge, and end to solve five key problems of edge computing [25]: cloud-edge collaboration, heterogeneous support, large-scale device access, lightweight edge and end, and consistent experience. The edge-cloud project OpenYurt [26] of CNCF extends the native Kubernetes to the intelligent open platform of edge computing, which ensures non-invasive standardization to realize edge autonomy and central cloud control. The decomposition technique based on the Martinez-Silva is put forward, intended for obtaining all the minimal support p-invariants of a Petri net. Among such invariants, the sets of places corresponding to the SMCs will be found [27]. Reference [28] proposes an SPN model to represent the MEC architecture and evaluate the trade-off between the MRT (mean response time) and resource utilization. The architecture is composed of three parts: mobile devices, front end, and edge computing; the resources of single servers are parallelized using containers. The main objective is to minimize resource costs and maximize performance. A blockchain-based decentralized solution for service composition [29] has been introduced in the scope of complex multimedia service delivery. Reference [30] proposed a collaborative framework at the network edge, aiming for a swift composite service delivery system and service composition models. A simulation-based optimization method using the SPN model for service composition [31] was put forward. Reference [32] highlights both QoS (Quality of Service) and QoE (Quality of Experience) and solves the service composition in an edge computing environment with a special focus on fault tolerance. The work in [33] focuses on workflow processes with concurrent behavior, which uses an extended version of the \(\alpha\) algorithm to incorporate timing information [34]. Process mining can be seen as a tool in the context of BPI (business process intelligence) [35], and transition systems can be represented by compact Petri nets [36]. PAIS (process-aware information systems) by process mining discovers process models from event logs, analyzes performance characteristics of processes, and establishes behavioral relations between Petri nets and BPMN (business process model and notation) models in order to visualize metrics within a BPMN diagram. The Petri net (free-choice workflow nets) and workflow graphs deal with \"high-level\" process models (e.g., BPMN models, control flow models, data, and resource perspectives) [37]. The conversion algorithms help to construct flat control flow skeletons of the target BPMN models from the discovered Petri nets and other \"low-level\" models, covering both the control flow perspective and the resource perspective [38]. A framework [39] is proposed with core components (constraintformula) enabling the constraint monitor. More tailor-made rules can be formalized into Petri-net patterns [40] or linear temporal logic to evaluate whether process executions comply with them. The model-based and clustering-based approaches learn the rules by analyzing event data. The constraint formula can be extended to predict and evaluate future violations.