This paper presents a technique to enhance the fidelity of business process simulation models by detecting unexplained (extraneous) delays from business process execution data, and modeling these delays in the simulation model, via timer events. The presentation was delivered at the 4th International Conference on Process Mining (ICPM'2022). Paper available at: https://arxiv.org/abs/2206.14051

1. Modeling Extraneous
Activity Delays in Business
Process Simulation
David Chapela-Campa
Marlon Dumas
4th International Conference on Process Mining
ICPM 2022

2. Modeling Extraneous Activity Delays in Business Process Simulation 2
Introduction

3. Business Process Simulation (BPS)
3
BPS allows users to address “what-if” analysis questions.
What would be the cycle time of the process if the rate of arrival of new cases
doubles?
Modeling Extraneous Activity Delays in Business Process Simulation

4. Business Process Simulation (BPS)
4
Traditionally, BPS models are manually created by modeling experts
However, this task is time-consuming and error-prone.
Modeling Extraneous Activity Delays in Business Process Simulation

5. Business Process Simulation (BPS)
5
To tackle this shortcoming, several studies have advocated for the use
of process mining techniques to automatically discover BPS models
from business process event logs.
Modeling Extraneous Activity Delays in Business Process Simulation

6. Business Process Simulation (BPS)
6
However, current automated BPS model discovery techniques assume
that all the waiting time is caused by:
Resource unavailability (e.g. resources being off-duty).
Resource contention (all resources who can perform an activity instance are
busy).
Modeling Extraneous Activity Delays in Business Process Simulation

7. Business Process Simulation (BPS)
7
It has been studied that a large proportion of waiting time in real
processes is caused by external factors not explicitly recorded in the
event log.
Modeling Extraneous Activity Delays in Business Process Simulation

8. Research Question
Modeling the extraneous waiting times during automated BPS model
discovery leads to BPS models that better reflect the temporal
performance of the process.
8
Modeling Extraneous Activity Delays in Business Process Simulation

9. Modeling Extraneous Activity Delays in Business Process Simulation 9
Proposal

10. Proposal
Let’s assume, for a moment, that each activity is preceded by an
extraneous delay and let’s capture this delay by means of timer event.
10
Modeling Extraneous Activity Delays in Business Process Simulation

11. Question: When does the extraneous delay start?
11
Modeling Extraneous Activity Delays in Business Process Simulation

12. Estimate optimal start times
Using the resource availability timeline, let’s determine the time point
when the resource became available to handle each activity instance.
12
Modeling Extraneous Activity Delays in Business Process Simulation

13. Estimate optimal start times
Using the resource availability timeline, let’s determine the time point
when the resource became available to handle each activity instance.
13
Modeling Extraneous Activity Delays in Business Process Simulation

14. Estimate optimal start times
Using the resource availability timeline, let’s determine the time point
when the resource became available to handle each activity instance.
14
Modeling Extraneous Activity Delays in Business Process Simulation

15. Estimate optimal start times
Using the resource availability timeline, let’s determine the time point
when the resource became available to handle each activity instance.
15
Modeling Extraneous Activity Delays in Business Process Simulation

16. Estimate optimal start times
Using the resource availability timeline, let’s determine the time point
when the resource became available to handle each activity instance.
16
Modeling Extraneous Activity Delays in Business Process Simulation

17. Estimate optimal start times
Now, looking at the sequence of activity instances in each case, ;et’s
determine the enablement time of each activity instance, i.e. when did
the activity instance became ready to be executed.
17
Modeling Extraneous Activity Delays in Business Process Simulation

18. Estimate optimal start times
Now, looking at the sequence of activity instances in each case, ;et’s
determine the enablement time of each activity instance, i.e. when did
the activity instance became ready to be executed.
18
Modeling Extraneous Activity Delays in Business Process Simulation

19. Estimate optimal start times
Now, looking at the sequence of activity instances in each case, ;et’s
determine the enablement time of each activity instance, i.e. when did
the activity instance became ready to be executed.
19
Modeling Extraneous Activity Delays in Business Process Simulation

20. Estimate optimal start times
Now, looking at the sequence of activity instances in each case, ;et’s
determine the enablement time of each activity instance, i.e. when did
the activity instance became ready to be executed.
20
Modeling Extraneous Activity Delays in Business Process Simulation

21. Estimate optimal start times
The optimal (or earliest) start time is the latest of the resource
availability time and the activity enablement time.
21
Modeling Extraneous Activity Delays in Business Process Simulation

22. Proposal
22
Modeling Extraneous Activity Delays in Business Process Simulation

23. Calculate extraneous activity delays
Compute extraneous delay: Interval from the optimal start to the
recorded start.
23
Modeling Extraneous Activity Delays in Business Process Simulation

24. Calculate extraneous activity delays
Now, for each activity instance, let’s compute its extraneous delay: the
time interval from the optimal start to the recorded start.
24
Modeling Extraneous Activity Delays in Business Process Simulation

25. Calculate extraneous activity delays
Model the duration as a non-linear function.
Duration distribution
25
Modeling Extraneous Activity Delays in Business Process Simulation

26. Calculate extraneous activity delays
However, the resource can be assigned to another activity while the
current one is waiting, eclipsing the delay.
26
Modeling Extraneous Activity Delays in Business Process Simulation

27. Calculate extraneous activity delays
However, the resource can be assigned to another activity while the
current one is waiting, eclipsing the delay.
27
Modeling Extraneous Activity Delays in Business Process Simulation

28. Calculate extraneous activity delays
However, the resource can be assigned to another activity while the
current one is waiting, eclipsing the delay.
28
Modeling Extraneous Activity Delays in Business Process Simulation

29. Calculate extraneous activity delays
What we calculated before may or may not be correct. It’s a heuristics!
So, let’s use an optimizer (Tree-structured Parzen Estimator – TPE) to
adjust the extraneous delays via scaling.
[α1, α2, …, αn]
Scale timers
Run
Simulation
Measure
Similarity
TPE
Optimizer
Discovered
Extraneous
Delays
Scaled
Extraneous
Delays
29
Modeling Extraneous Activity Delays in Business Process Simulation
α1 x
α2 x
α3 x
1.8 x
2.5 x
1.0 x

30. Proposal
30
Modeling Extraneous Activity Delays in Business Process Simulation

31. Enhance BPS Model
Edit the BPMN model by inserting a timer prior to each activity. The
duration distribution of the timer event, captures the observed
extraneous delays.
31
Modeling Extraneous Activity Delays in Business Process Simulation

32. Modeling Extraneous Activity Delays in Business Process Simulation 32
Evaluation

33. Experiment 1
33
Modeling Extraneous Activity Delays in Business Process Simulation
Measure the accuracy of the re-discovery of timer events.
4 simulated processes with no timers, one timer, and four timers.
Real simulation log with already defined timers.

34. Experiment 1
34
Modeling Extraneous Activity Delays in Business Process Simulation
4 simulated processes with no timers, one timer, and four timers.

35. Experiment 1
35
Modeling Extraneous Activity Delays in Business Process Simulation
Real simulation log with already defined timers.

36. Experiment 2
36
Modeling Extraneous Activity Delays in Business Process Simulation
Evaluate the improvement of the simulation in real-life scenarios.

37. Experiment 2
Cycle time EMD
Timestamp distribution EMD
Modeling Extraneous Activity Delays in Business Process Simulation 37

38. Experiment 2
Cycle time EMD
Timestamp distribution EMD
38
Modeling Extraneous Activity Delays in Business Process Simulation

39. Modeling Extraneous
Activity Delays in Business
Process Simulation
david.chapela@ut.ee
marlon.dumas@ut.ee
4th International Conference on Process Mining
ICPM 2022

40. Experiment 2
• BPIC2012 and BPIC2017.
• Temporal split in training
and test.
40
Modeling Extraneous Activity Delays in Business Process Simulation

41. Experiment 2
• BPIC2012 and BPIC2017.
41
Modeling Extraneous Activity Delays in Business Process Simulation

42. Future Work
• Estimate the trace inter-arrival time to discover the extraneous
waiting times associated to the first activity of each trace.
• Use resource availability calendars to consider the resources as
unavailable when they are out of their working hours.
• Propose extraneous delays dependent on the previous and following
activities.
42
Modeling Extraneous Activity Delays in Business Process Simulation