## 5 Process Mining for EIS
Multi-sets are also used to present the states of Petri nets and BPMN models. The performance information for a Petri net can be visualized in the initial BPMN model to show the behavioral properties of process models discovered from an event log, and language relations between Petri nets and corresponding BPMN. Subsequently, performance analyses provide the metrics, such as case arrival rate and average duration of the activities, which aim to provide a simulation model and the corresponding simulated event log as close to reality as possible. Existing process mining tools provide users with a visual representation of process discovery and performance analyses using event data in the form of event logs, which include three main modules: process mining using mining algorithm (Algorithm \(\alpha\)), simulation representation (BPMN), and transformation of the generated events into an event log. BPMN packages architecture and their functionality in the tool, such as ProM or Disco, provides the ability to convert Petri nets, transition, and causal nets to BPMN. Moreover, the resource and data flow perspectives can be discovered as well: Process trees with resources can be converted to the BPMN model with lanes, and data Petri nets by the data-aware process mining algorithm can be used to create BPMN models with data perspective. The EIS is instantiated in a ProM plug-in, whose input objects are event logs shown in Table 2:  
Figure 4: Architecture of Process Mining for EIS. The process miner includes the following three aspects: 1 log summary: learn about process event classes and their related properties in the dashboard, inspector, and summary; 2 discovering processes: the model is mined into a Petri net by process mining algorithm; 3 modeling for visualization: replays a log to obtain performance information, and enhances the process. The event logs in Table 1 are expressed as \(L=[ABCD^{3},ACBD^{3},AED^{4}\ldots]\) according to Formula (1). Its event occurrences (absolute/ relative) are as follows: A = 10/27.8%, B = 6/16.7%, C = 6/16.7%, D = 10/27.8%, E = 4/11.1%. The results mined by Alpha Miner and the inductive visual miner for an EIS instance are shown in Figure 5:  
The above process mining implementation for EIS can discover processes such as proof-of-concept, to enhance and optimize the business processes. The experimental results highlight the research:  
* Rule monitors effectively detect violations to analyze future events through context, formula, and rule;
* Service engine effectively generates corresponding actions to assess future rule instances, with business (activity/operation) and formula;
* The application from event data improves business processes by process discovery. Process mining can achieve structural models preserving behavior recorded in an event log on the control flow perspective; Petri nets, causal nets, and the transition system are generated from an event log by various control flow discovery algorithms. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Trace** & **Name** & **Org** & **Time** & **State** \\ \hline
1 & A & JIT & 2022-01-08T08:20:01 & complete \\ \hline
1 & B & JIT & 2022-01-08T08:21:01 & complete \\ \hline
1 & C & JIT & 2022-01-08T08:22:01 & complete \\ \hline
1 & D & JIT & 2022-01-08T08:23:01 & complete \\ \hline
2 & A & JIT & 2022-01-10T08:20:01 & complete \\ \hline... & & & & \\ \hline
3 & A & JIT & 2022-01-12T08:20:01 & complete \\ \hline... & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Event Log. Figure 5: Models mined in ProM.