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Erlang C

別名： Erlang C formula

Erlang C is a queuing formula that calculates the probability an arriving call has to wait, and from that the agents required to answer a given volume within a target time.

It models a queue where calls arrive at random and wait until an agent is free. Feed it offered load and a service-level target and it returns the minimum agents needed, along with the service level, average speed of answer and occupancy any given headcount would produce.

Erlang C rests on four assumptions, and all four break in real operations: calls arrive at random (Poisson), no caller ever abandons, every agent handles every call identically, and conditions hold steady across the interval. The no-abandonment assumption is the consequential one — where callers do hang up, Erlang C over-staffs, and Erlang A exists to correct for it.

Erlang C is distinct from Erlang B, which models systems with no queue at all — a blocked call is simply lost. Erlang B is the right model for trunk sizing; Erlang C is the right model for agent staffing. In practice Erlang C is computed via the Erlang B recurrence, which stays numerically stable at headcounts where the textbook factorial form overflows.

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Erlang C staffing calculator

よくある質問

What is the difference between Erlang B and Erlang C?

Erlang B models systems with no queue — a call that finds every line busy is lost. Erlang C models systems where calls queue and wait. Use Erlang B for trunk and line sizing, Erlang C for agent staffing.

When should you not use Erlang C?

When abandonment is high, because Erlang C assumes nobody hangs up and will over-staff as a result. Also when routing is skills-based, since a single pooled calculation understates what each skill group needs, and when arrivals spike sharply inside the interval you are modelling.

関連用語

ErlangThe unit of telephone traffic. One Erlang is one hour of calls per hour — a single line occupied continuously.Service levelThe share of calls answered within a target time — commonly 80% within 20 seconds. A convention rather than a standard, despite how often it is quoted as one.Average handle timeThe average time an agent spends on a contact end to end — talk time plus hold time plus after-call work. The core input to every staffing calculation.OccupancyThe share of logged-in time an agent spends handling contacts. Healthy between 75% and 85%; sustained higher figures drive burnout and attrition.ShrinkageThe share of paid time agents are not available to take contacts — breaks, training, meetings, absence. Typically 30%, and the reason rostered headcount exceeds calculated agents.

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