Erlang B / C Calculator
Traffic engineering for circuit-switched networks (Erlang B) and call centres (Erlang C).
GOS = Grade of Service (blocking probability). Typical target: 2% for PSTN trunk groups.
3GPP · ITU-R · Okumura-Hata · COST-231
Erlang B and Erlang C Formulas
Both models characterise a system offered A Erlangs of traffic with N circuits or agents. Traffic intensity is A = λ/μ, where λ is the call arrival rate and μ is the service rate (1/average call duration).
Erlang B — Blocking probability (lost calls)
B(A, N) = (AN / N!) / Σk=0..N (Ak / k!)
Erlang C — Delay probability (queued calls)
C(A, N) = [AN/N! × N/(N−A)] / [Σk=0..N−1(Ak/k!) + AN/N! × N/(N−A)]
Average queue wait time
W = C(A, N) × AHT / (N − A)
AHT = Average Handle Time in seconds. Valid only when A < N.
Frequently Asked Questions
What is traffic intensity in Erlangs?▾
One Erlang represents a single circuit occupied continuously for one hour. Traffic intensity A = λ × h, where λ is the average number of calls per second and h is the average call duration in seconds. For example, 10 calls per hour each lasting 6 minutes = 10 × (6/60) = 1 Erlang.
When should I use Erlang B vs Erlang C?▾
Use Erlang B for circuit-switched networks (PSTN trunk groups, GSM) where blocked calls are simply rejected and the caller must try again. Use Erlang C for queued systems such as call centres or packet schedulers where calls wait in a queue rather than being dropped.
What is Grade of Service (GOS)?▾
GOS is the blocking probability — the fraction of call attempts that are blocked due to all circuits being busy. A typical PSTN GOS target is 2% (B = 0.02), meaning no more than 2 in 100 call attempts are blocked during the busy hour.
Why must traffic be strictly less than the number of agents in Erlang C?▾
The Erlang C model assumes an infinite queue but finite servers. If offered traffic A ≥ N agents, the queue grows without bound — no steady-state exists and average wait time is infinite. The system is mathematically unstable. In practice, target utilisation of 80–85% (A/N ≤ 0.85) is recommended.