Exclusive gateway (XOR)
The weighted expected value and how scenarios are generated.
At an exclusive gateway, each case takes only one branch. The question is no longer “how long does it take” but “how long does it take on average”.
The formula
This is the familiar mathematical expectation: a probability-weighted average. Cost uses exactly this formula with Ci.
Example
After the requisition step, the process branches on the order value:
| Branch | Probability | Time |
|---|---|---|
| ≤ 50 million — team leader approves | 75% | 45 minutes |
| > 50 million — director approves | 25% | 180 minutes |
No case takes exactly 78,75 minutes — they take 45 or 180. The expected number is for resource planning; to commit to a customer you have to look at P90.
How the expected value differs from the scenarios
An exclusive gateway generates several scenarios, each one a real path with its own probability. The tool shows both points of view:
| View | Gives | Use when |
|---|---|---|
| Expected value (formula 4) | A single number | Budgeting, capacity planning |
| The scenario list | Fastest / slowest / each individual path | Understanding why the difference exists |
| Simulation | A distribution, P90 | Committing to an SLA |
The branches are split evenly. Two branches become 50/50 — rarely true in practice, so fill in the real number as soon as you have it. See Branch probabilities for how they are normalised when the declaration is incomplete.
Inclusive gateway (OR)
An OR gateway allows one or more branches to run together. Because which combination of branches runs depends on real data the model does not have, the tool currently handles OR as AND: assuming every branch runs. This is a conservative estimate — time and cost will not be undercounted.