Erlang B Calculator

How it works

B(E, m) = (E^m ÷ m!) ÷ Σₖ₌₀ᵐ (E^k ÷ k!) · computed by the stable recursion B(0) = 1, B(k) = E·B(k−1) ÷ (k + E·B(k−1)) · carried traffic = E × (1 − B) · E = calls per hour × average holding time (h)

The Erlang B formula (A. K. Erlang, 1917) gives the probability that a call arrives to find every line busy and is lost, assuming random (Poisson) call arrivals, blocked calls that are cleared rather than queued, and the busy-hour traffic in erlangs. It is the standard way to size PBX trunks, SIP channels, radio channels and dial-up modem pools; a grade of service of 1% (P.01) is the common target. For calls that wait in a queue instead of being blocked — call centres — use Erlang C.

Worked example

With 10 erlangs of busy-hour traffic offered to 15 lines, the blocking probability is 3.650%, so 9.635 E is carried, 0.365 E is lost and each line is busy 64.2% of the time on average. Holding blocking to 1% needs 18 lines.

Sources: ITU-T Recommendation E.520 — Number of circuits to be provided in automatic and/or semi-automatic operation · Wikipedia — Erlang (unit): Erlang B formula

Frequently asked questions