# Behavioral and Performance Analysis of a Real-Time Case Study Event Log: A Process Mining Approach
## 4 Discovery Analysis
### In-Depth Analysis: Tracking Process Inefficiencies
Heuristic miner generates a heuristic net that can be converted into other process models, such as a Petri net, for further analysis. To avoid the constraints and solve the problem of the alpha algorithm, the heuristic miner algorithm was applied to the log data as it is more sophisticated and adequate  
Figure 7: (**a**) Petri net generated by alpha miner on the original log data and (**b**) Petri net generated by alpha miner after preprocessing. than the alpha algorithm. Using this algorithm, we wanted to generate a model that would be less sensitive to the incompleteness of the log data and the log containing the noise. Frequencies are considered in the heuristic miner algorithm compared to the alpha algorithm. Figure 8 shows the heuristic net model created by applying this algorithm, and frequencies are also shown in this model. Although the resultant model represents a more sophisticated view of the process flow than the alpha algorithm, the produced model cannot correctly deal with mixed and complex data. Moreover, due to missing connections or activities, the results produced by heuristic mining give less meaningful information about the process. **Fuzzy Miner**  
The third discovery algorithm that was applied to overcome the limitations of the heuristic miner was the fuzzy miner [40]. The fuzzy miner is one of the younger process discovery algorithms. It is suitable for mining less structured processes with many activities and highly unstructured and conflicting behavior and interactively simplifies the model; i.e., it shapes spaghetti-like models into more concise ones. This algorithm is more sophisticated than the heuristic miner because it can deal with more complex structures that need to be more easily comprehensible at first glance. Figure 9 shows the fuzzy model of the log data. In this generated fuzzy model, the arrows' thickness represents the absolute frequency of occurrences. It shows all the activities as well as their casual dependencies. However, it can be seen in this model that some exceptional behaviors and loops show the repetition of activities in the data, which means there is a need to pre-process the data. Figure 8: (**a**) Petri net generated by fuzzy miner on the original noisy data, and (**b**) Petri net generated by heuristic net on refined data. These Petri nets now fully explained the process flow in optimized form. After the control flow analysis, the performance analysis was carried out to find the issues related to the time stamp in order for us to analyze the things that still had an impact on the process flow. Figure 9 shows the performance map of the procurement process in Disco, and from it, we recognize the activity path that consumes the maximum time and affects the performance. In the Disco tool, several options related to time are shown in Table 12. In this table, the first column shows the activity paths across which time is measured, and in this column, 'C' represents the activity'requisite budget confirmation', and 'R' represents the'requisite budget reservation'. Here, the total duration shows the highly impacted areas for delays in our process by giving the cumulative times (time taken by adding up the overall cases) for each path between activities. Alternatively, the mean duration gives the average time spent between activities. The maximum duration measures the most considerable execution time and delays in flow, and the minimum duration gives the minimum execution time taken between activities. These measures show that the maximum time consumption and delay are in the path'requisite budget confirmation purchase requisite approved I'.