Count the same waiting time two ways
Three visitors enter at minutes 0, 2 and 4. Each stays for the duration you choose. The observation ends when the last visitor leaves. Arrivals at time zero count as inside immediately.
| Visitor | Arrival | Departure | Time inside |
|---|
Multiply the average arrival rate by the average time inside. Compare it with average occupancy. The equality comes from counting total person-minutes, rather than from an assumed random arrival pattern.
This is an invented finite accounting example. It has no single-server rule, rejection, abandonment or startup backlog. It does not predict how quickly a café can serve people, or how their durations change when more people arrive.