Process Mining shows parallelism in the frequency view, with numbers in parenthesis above transitions.
But what does this really mean?
Let's start with a simple case (case 1).
- A1 starts the case
- A2 starts after A1, and includes an end-date (service time = 5 min)
- A3 and A4 start 1 minute after A2, with no end-date.
- A5 starts 10 min after A1.
In this case, A3 and A4 are executed in parallel with A2.

Load this event log: Parallelism-case1.csv to see how parallelism is displayed in Process Mining.
A3 and A4 start after A2, but occur during A2. Therefore they are indicated as parallel activities with a transition from A1.
- 1(1) on A1->A2 says that there is one occurence with 1 parallelism. Same for 1(1) on A1>A3
- A4 follows A3, therefore there is a simple A3->A4 transition.
- Then the parallelism merges into A5. This is shown with 1(1) on the transitionS A2->A5 and A4->A5
You should see this process model:

As expected, the generated BPMN model shows the parallelism with the 2 AND gateways:

Let's now add a second case that contains a new activity A4-bis that starts after A2 completes. Case 2 looks like this:

Load this event log: Parallelism-case2.csv
We now see 2(2) on A1-A2 and on A1-A3 because we have 2 cases with parallelism in each.
As expected, one parallelism merges in A5 (case 1), and the other one merges in A4-bis (case 2).
This is shown with 1(1) on A2-A5 // A4-A5 for case 1; and with 1(1) on A2-A4bis // A4-A4bis

To complete this blog, let's see what happens if a third case is added, with no parallelism.
Case 3 looks like case 1, but A3 and A4 start after A2 terminates.

Load this event log:
Parallelism-case3.csv
- 3(2) on A1->A2 says that we have 3 cases with 2 parallelisms (case 1 and 2).
- 2(2) on A1->A3 says that we have 2 cases with 2 parallelisms (case 1 and 2).
- We have 1 transition on A2-A3 for case 3.
- 2(1) on A4->A5 says that we have 2 transitions and 1 parallelism (case 1). The direct transition is for case 3.
- As in the precedent diagram, case 2 merges in A4-bis.

When you have a transition with parallelism shown as a parenthesis, you can filter the cases with parallelism directly from the diagram.
From now on, you should better understand this concept and how it is represented and used in IBM Process Mining. Make your own experiments, and share!