Why adding a person didn't help
A support desk, simulated one call at a time. Set the arrival rate, the average handle time, and the headcount — then watch what happens to the wait as utilisation climbs past about 85%. The curve is the point.
A support desk, simulated one call at a time. Set the arrival rate, the average handle time, and the headcount — then watch what happens to the wait as utilisation climbs past about 85%. The curve is the point.
Each square is an agent; each tick to the left is a caller waiting. Watch the queue, not the agents — busy agents look identical at 70% and at 95%.
Wait against utilisation at this handle time. The lower line is the same desk with one more agent. The gap between them is what that person actually buys you.
The reason this feels wrong. Utilisation is a comfortable number — 92% sounds like a well-run desk, and 70% sounds like slack you should cut. But the wait doesn't rise in proportion to the load; it rises in proportion to 1/(1−ρ). Going from 70% to 92% doesn't add a third to the wait. It multiplies it. The same arithmetic in reverse is why the extra agent seems to do nothing at 70% and works like magic at 92% — and why a desk run at "full efficiency" is a desk one sick day away from a crisis.