Calculate the probability of call blocking for a given number of trunks and traffic load.
The Erlang B formula calculates the probability that an incoming call finds all trunks/channels busy and is blocked, given a fixed number of trunks (N) and offered traffic (A) in Erlangs, assuming blocked calls are lost (not queued or retried) — the standard model for circuit-switched trunk groups. It's computed recursively: B(0,A) = 1, and B(n,A) = (A × B(n-1,A)) / (n + A × B(n-1,A)) for each trunk added, which avoids the numerical overflow that computing factorials directly would cause for larger trunk counts.
Erlang B formula
B(N,A) = (A^N / N!) / Σ(A^k / k!, k=0..N)
Recursive form (used for computation)
B(n,A) = (A × B(n-1,A)) / (n + A × B(n-1,A)), with B(0,A) = 1
1-2% (often called P.01 or P.02 grade of service) is a common target for enterprise voice trunks — meaning roughly 1-2 calls per 100 offered during the busy hour would be blocked. Emergency services and critical infrastructure often target well below 1%, while cost-sensitive or non-critical applications may tolerate 5% or higher.
Erlang B assumes blocked calls are simply lost (the caller hears a busy signal or fast busy and must redial) — the standard model for PSTN trunk groups. Erlang C instead assumes blocked calls queue and wait for the next available channel, which better models call center agent staffing where callers are placed on hold rather than disconnected.
There's no fixed ratio — it depends on where you are on the Erlang B curve. Near saturation (blocking already high), even one additional trunk can meaningfully cut blocking; near very low blocking, the curve flattens and each additional trunk buys progressively smaller improvements. Recompute with N+1, N+2, etc. to find the exact trunk count that hits your target grade of service.