Wait Desk

Read a queue's four numbers and see what they actually produce. Utilisation is arrivals x service / workers, and the wait is rho/(1-rho) times the service time: 1x at 50%, 4x at 80%, 9x at 90%, 19x at 95%, 99x at 99% - and the service time never changed. So the same five points of load cost 1.22x from 50% and 6.32x from 94%: "keep it under eighty percent" is a rule that fails exactly where it is needed. A backlog drains at the SPARE capacity, not the capacity, so an outage takes the SAME rho/(1-rho) times as long to clear as it lasted - a one-minute stop at 90% is nine minutes of recovery. Pooling beats utilisation: at the same 90%, one worker waits 900ms and fifty wait 7.28ms, with identical load per worker. Variability costs as much as the mean. And retries are arrival rate - every attempt is a real job, so a failure rate multiplies the arrivals by 1 + p + p^2, not by the attempt count, and a queue at 90% has only 10% of headroom for it. Five lanes over one queue sheet: size a queue that meets its target, read what an existing one waits and how deep it gets, price the wait and the backlog, and decide what to change. Free browser-side Erlang C, Little's Law and Kingman - nothing is measured and no queue is inspected.

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