Erlang C

Erlang C is the queueing formula, published by Danish engineer A.K. Erlang in 1917, that still sits inside nearly every workforce-management tool. Feed it your forecast call volume, your average handle time, and a target service level, and it returns the probability that a caller has to wait — and therefore how many agents you need on the phones to keep that wait acceptable.

The engine is traffic intensity, measured in Erlangs: arrival rate multiplied by handle time. From that and a candidate headcount, the formula computes the odds of queuing; you add agents until that probability is low enough to hit your goal (say, 80% of calls answered within 20 seconds). It rests on tidy assumptions: calls arrive at random (a Poisson process), handle times are exponentially distributed, service is first-come-first-served, and — the load-bearing one — callers are infinitely patient and never hang up.

What it hides: nobody is infinitely patient. Because Erlang C assumes zero abandonment, it overstates staffing when queues are calm, which is a safe, conservative bias — it rarely tells you to under-hire. But it fails perversely under stress: when you are short-staffed, real callers abandon, apparent volume drops, and the model then concludes you need fewer agents, hiding the very shortage that is driving people away. It also ignores shrinkage, multi-skilling, channel concurrency, and blended work — so its raw output is a starting floor, not a finished schedule.