Erlangs in Telecommunications
Erlangs are a unit used in telecommunications to measure traffic load or how busy a system is.
Named after Danish mathematician and engineer Agner Krarup Erlang.
Simple Meaning
1 Erlang = one communication channel fully used for 1 hour
- 1 call lasting 1 hour → 1 Erlang
- 2 calls lasting 30 minutes each → 1 Erlang
- 60 calls lasting 1 minute each → 1 Erlang
Formula
Traffic (Erlangs) = (Number of calls × Average call duration) / Time period
Why It’s Important
- Design telephone networks
- Avoid congestion
- Determine number of channels needed
Real Example
If 120 calls happen in 1 hour and each call lasts 3 minutes:
Traffic = (120 × 3) / 60 = 6 Erlangs
Erlang B (Blocking Probability)
Used when blocked calls are cleared (no waiting).
Common in traditional telephone systems.
B(A, N) = (A^N / N!) / ฮฃ (k=0 to N) (A^k / k!)
- A = traffic in Erlangs
- N = number of channels
- Gives probability that a call is blocked
Erlang C (Waiting Probability)
Used when blocked calls are queued (waiting allowed).
Common in call centers.
C(A, N) = [(A^N / N!) × (N / (N - A))] / [ฮฃ (k=0 to N-1)(A^k / k!) + (A^N / N!) × (N / (N - A))]
- A = traffic in Erlangs
- N = number of servers/channels
- Gives probability that a call has to wait
Key Differences
- Erlang B: No waiting, blocked calls are lost
- Erlang C: Calls wait in queue
Summary
- Higher Erlangs = busier system
- Used for network planning and optimization