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.
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.
Erlang B Capacity Reference — 2 % GOS
Minimum number of circuits required to carry a given traffic load at 2 % blocking (Grade of Service = 0.02) per the Erlang B model. Used to size GSM TCH groups, PSTN trunk groups, and IMS media bearers.
| Traffic (Erlang) | Circuits needed | Typical scenario |
|---|---|---|
| 0.5 E | 3 | ~25 subscribers, 20 mE each |
| 1.0 E | 5 | ~50 subscribers, 20 mE each |
| 2.0 E | 7 | Small BSC sector |
| 5.0 E | 10 | GSM cell, low density |
| 10.0 E | 17 | GSM macro cell, typical |
| 15.0 E | 23 | Urban macro cell |
| 20.0 E | 29 | Dense urban cell |
| 30.0 E | 41 | High-capacity cell |
| 50.0 E | 63 | PSTN trunk group |
Worked Example — GSM Cell TCH Dimensioning
A GSM 900 cell is expected to serve 300 subscribers during the busy hour. Each subscriber generates 25 mE (0.025 Erlang) of voice traffic. Size the Traffic Channel (TCH) group for 2 % GOS.
Step 1 — Total offered traffic.
A = 300 × 0.025 = 7.5 Erlang
Step 2 — Apply Erlang B at B = 0.02. From the table (or calculator above): 7.5 E at 2 % GOS requires 13 circuits.
Step 3 — GSM timeslot allocation. 13 TCH + 1 BCCH/CCCH = 14 timeslots = 2 transceivers (TRX) on the 2/2/2 GSM configuration.
To go further and estimate how many subscribers a cell can support across all RRC states (not just circuit-switched voice), use the subscriber capacity calculator. For VoLTE call capacity in LTE, see the VoLTE capacity calculator.
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.