Erlang Models
Definition
Erlang Models
Erlang models are mathematical formulas that predict how many staff, lines, or trunks a call center needs to meet expected traffic. Named after Danish mathematician Agner Krarup Erlang, the three main variants (Erlang A, B, and C) turn call volume and average handle time into concrete workforce forecasts.
Erlang published the original traffic equations in 1909 while working at the Copenhagen Telephone Company. Over a century later, his math still sits inside almost every workforce management suite scheduling voice agents. The formulas outlived rotary dials, IVR, and the pivot to cloud contact centers.
The reason is simple. Call arrivals behave randomly, and random arrivals need probability, not averages. An erlang is one hour of continuous circuit use. Feed enough of them into the right formula, and you get a defensible staffing number for the next quarter-hour.
Key takeaways
- Erlang models convert call volume and handle time into staffing and trunking numbers.
- The three variants split by caller behaviour: A allows abandon, B blocks, C queues.
- Erlang C remains the default engine in most workforce management platforms in 2026.
- Every model assumes Poisson arrivals, so a bad forecast breaks the whole calculation.
How it works
Erlang models feed three inputs into a probability formula: call arrival rate, average handle time, and target service level. The output is the number of agents or trunks needed to meet that target. Each variant handles caller behaviour differently.
Every model assumes calls arrive randomly according to a Poisson distribution. That distribution is what makes Erlang math predictive rather than a guess. Feed a bad arrival rate in, and the whole staffing plan misses by an entire shift.
Handle time matters just as much. If your average handle time creeps from four to five minutes, the same call volume needs roughly 25% more agents at the same service level. Small drift in the inputs produces large drift in the headcount.
| Input | What it means | Typical range |
|---|---|---|
| Call arrival rate (λ) | Calls per interval | 30–300 per 30-min block |
| Average handle time | Talk time plus after-call work | 3–7 minutes |
| Service level | % answered within X seconds | 80/20 is the standard target |
| Shrinkage | Time agents are not on the phone | 30–35% |
The three named formulas each answer a different question. Erlang B asks how many trunks you need before a caller hits a busy tone. Erlang C asks how many agents you need before a caller waits too long. Erlang A extends C by modelling abandonment, which matters when patience is short.
Examples
Contact centers across banking, healthcare, and retail run Erlang C daily. Workforce planners at global BPOs plug quarter-hourly forecasts into Erlang engines to schedule agents down to fifteen-minute intervals, then reforecast intraday when volumes drift from plan.
- HSBC’s global contact centers staff their multilingual queues using Erlang C forecasts, adjusted quarter-hourly for shrinkage and skill mix.
- Amazon Connect shipped an Erlang-C based forecasting module inside its cloud contact center product in 2022, and refined the model through 2025 releases.
- Philippine BPOs supporting US retail clients apply Erlang B to size SIP trunks ahead of Black Friday and Cyber Monday spikes.
- NICE and Verint workforce management suites embed Erlang models as their default scheduling engine, layered with what-if scenario tooling on top.
Related terms
Erlang math ties into every discipline that touches call volume, agent hours, or line capacity. The adjacent glossary entries below anchor the wider workforce and contact center vocabulary that Erlang planning quietly depends on.
- Call center: the operation Erlang models size and staff.
- Agents: the frontline headcount Erlang C forecasts.
- Workforce management: the wider discipline Erlang feeds forecasts into.
- Average handle time: one of two required inputs alongside arrival rate.
- Service level agreement: the answer-time target Erlang C solves for.
- Business process outsourcing: the sector that industrialised Erlang scheduling at scale.
FAQ
What is the difference between Erlang B and Erlang C?
Erlang B assumes callers who hit a busy signal disappear and never call back. Erlang C assumes those callers wait in queue. B sizes trunks and lines; C sizes agent headcount.
Who invented the Erlang formulas?
Danish mathematician Agner Krarup Erlang first published the traffic equations in 1909 while working at the Copenhagen Telephone Company. Erlang A came later, developed in 1946 by Swedish engineer Conny Palm. See the Erlang unit reference) for the underlying math.
Is Erlang C still accurate for modern contact centers?
Erlang C remains the default in most workforce management suites, but it assumes infinite caller patience. For channels with fast abandonment such as chat and SMS, planners layer Erlang A or discrete-event simulation on top, as Call Centre Helper has documented in practitioner guides.
What service level does Erlang C target?
The industry-default target is 80/20, meaning 80% of calls answered within 20 seconds. Erlang C solves for the agent count that meets that threshold given the arrival rate and handle time you feed it.
Can Erlang models handle omnichannel workloads?
Not natively. Erlang was built for synchronous voice traffic. Chat, email, and asynchronous messaging need modified models or discrete-event simulation to reflect agent concurrency and multi-tasking behaviour.
How often should forecasts be refreshed?
Most mature BPOs reforecast in fifteen or thirty-minute intervals intraday, then rebuild the base forecast weekly. A stale forecast is the most common reason an Erlang-driven schedule misses service level.
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