A queue’s wait is not its service time.

Utilisation is arrivals × service ÷ workers, and the wait is ρ/(1−ρ) times the service time. That is 1× at fifty percent, 4× at eighty, 9× at ninety, 19× at ninety-five and 99× at ninety-nine — and the service time never changed. So the same five points of load cost 1.22× from fifty percent and 6.32× from ninety-four: “keep it under eighty percent” is a rule that fails exactly where it is needed.

The engine is free and needs no account, and it inspects nothing: every figure is arithmetic on four numbers you paste. A backlog drains at the SPARE capacity, not at the capacity, because the arrivals keep coming — so an outage takes the same ρ/(1−ρ) times as long to clear as it lasted. A one-minute stop at ninety percent is nine minutes of recovery, which is why “we were only down a minute” is a statement about the outage and not about the incident. Pooling beats utilisation: at the same ninety percent, one worker waits 900ms and fifty wait 7.28ms — with identical load per worker — so “we are at ninety percent” says nothing without the pool count. Variability costs as much as the mean: at the same ninety percent and the same 100ms mean, constant service waits 450ms and a heavy tail waits 4.95s. And retries are arrival rate — every attempt is a real job, so a failure rate multiplies the arrivals by 1 + p + p² + …, not by the attempt count, and a queue at ninety percent has only ten percent of headroom for it to consume. Every lane ships a worked example that costs nothing. Writing the report needs credits.