Predict what happens to waiting time as a system gets busier, which is not proportionally, and use that single relationship to size a service, set a timeout, choose a queue depth and explain why a system at ninety percent utilisation feels broken

Work That Waits in a Queue

Why a system at ninety percent busy has queues ten times longer than one at fifty. The arithmetic of waiting, and what to do about it.

8 lessons, written and corrected before you arrived. Reading them here needs no account. The first reads the whole way through; the others open and then stop, because a page nobody owns cannot tell who is reading it. Starting the course gives you your own copy, where every idea has problems standing under it and you can ask about any sentence.

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01Things Arriving, and Things Being ServedEvery waiting system is two rates, the rate work arrives and the rate it can be served. The whole subject starts with the condition that keeps the queue from growing forever.
02How Busy Is Busyopening onlyUtilisation is the share of time the servers are occupied. It is the number everybody reports and, taken on its own, it says almost nothing about how long anything waits.
03Why Waiting Explodes Near the Endopening onlyWaiting time does not rise in step with load. It rises gently and then vertically, so the last ten per cent of capacity costs more than the first ninety.
04Arrivals Come in Clumpsopening onlyThe same average arrival rate produces far longer queues when arrivals clump together, and the clumping is a measurable quantity rather than an adjective.
05One Queue or Severalopening onlyOne queue feeding many servers beats a separate queue for each one, and the reason is the idle server standing next to somebody who is waiting.
06The Average Is Not the Experienceopening onlyNobody experiences the average wait. What people notice is the slow end of the distribution, and a request made of many parts inherits the slow end of every one.
07When the Queue Fills Upopening onlyWhen arrivals exceed capacity the only choices are to queue, to shed, or to collapse. Choosing deliberately is the difference between a degraded service and no service.
08The One Relationship Worth Memorisingopening onlyThe number of things in a system equals the rate they arrive multiplied by the time each one stays. It assumes almost nothing, and it gives you whichever of the three you cannot measure.