Why does latency explode when the service is only 85% busy? Push utilisation from 70% to 95% and watch queue wait multiply, then make service times less predictable and watch it happen sooner. The demo needs JavaScript.
Going from 70% to 85% busy halves the headroom and roughly quadruples the wait. From 85% to 95% it does it again. "We are only at 85% CPU" is already a statement about latency.
Kingman's formula multiplies the wait by the variability of service times. A heavy tail at 80% can queue worse than predictable work at 95%: fix the slow requests before buying servers.
L = λW holds for any stable queue. When the number in the system and arrival rate × time in system disagree, the queue is not in steady state, usually because it is still growing.
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