Erlang Models
Definition
Erlang Models
Erlang models are formulas that predict how many staff, lines, or trunks a call center needs to meet expected traffic. They turn call volume and handle time into a staffing number you can defend, using probability rather than averages of past demand.
Agner Krarup 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 that schedules voice agents.
The formulas outlived rotary dials, interactive voice response (IVR) menus, and the pivot to cloud contact centers. The reason is simple. Call arrivals behave randomly — and random arrivals need probability, not averages.
One erlang is one hour of continuous circuit use, the unit set out in Erlang.com’s explainer on the erlang. Feed enough of them into the right formula and you get a 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.
- Business process outsourcing (BPO) planners inflate Erlang output by 30–35% shrinkage before publishing a roster.
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 agent or trunk count needed to hit that target. Each variant treats waiting callers differently.
Every model assumes calls arrive randomly, following a Poisson distribution. That assumption 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 — which is why careful planners audit handle time before anyone argues about headcount.
Run the arithmetic yourself. Two hundred calls in a 30-minute block at five minutes of handle time is 1,000 agent minutes of work, or roughly 33 erlangs of offered load.
Shrinkage then stretches that number. Strip out 30% of paid time for breaks, training, and coaching, and the same work needs about 43% more hours, because you divide the load by 0.7 instead of multiplying it by 1.3.
| Input | What it means | Typical planning range |
|---|---|---|
| Call arrival rate | calls per interval | 30–300 per 30-minute block |
| Average handle time | talk time plus after-call work | 3–7 minutes |
| Service level | share answered within X seconds | 80/20 is the standard target |
| Shrinkage | time agents are not on the phone | 30–35% |
| Blocking target (Erlang B) | share of callers who meet a busy tone | commonly set at 1% |
| Patience window (Erlang A) | how long a caller waits before hanging up | seconds, not minutes |
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.
Examples
Erlang C runs daily inside contact centers across banking, healthcare, and retail. Workforce planners at global BPOs push quarter-hourly forecasts through an Erlang engine, schedule agents to fifteen-minute intervals, then reforecast intraday when volume drifts.
- HSBC staffs its multilingual queues from Erlang C forecasts, adjusted quarter-hourly for shrinkage and skill mix across its global contact centers.
- Amazon Connect shipped an Erlang C based forecasting module inside its cloud contact center product in 2022, then refined the model through its 2025 releases.
- Philippine BPOs serving United States retail clients size their session initiation protocol (SIP) trunks with Erlang B ahead of Black Friday and Cyber Monday, holding blocking near the 1% design target.
- NICE and Verint ship Erlang models as the default scheduling engine inside their workforce management suites, with what-if scenario tooling layered on top.
- Healthcare appointment lines lean on Erlang A instead, because patients hang up quickly and Erlang C’s infinitely patient caller overstates how many will still be holding.
Each case starts in the same place: a volume forecast, a handle time, and a service target. Erlang turns those three numbers into a roster a planner can defend in a client review — not a hunch dressed up as a plan.
The reverse holds too. When a schedule misses service level three days running, planners re-test the inputs before they blame the model, because the arithmetic rarely breaks and the forecast often does.
Related terms
Erlang math touches every discipline that deals in call volume, agent hours, or line capacity. The entries below mark the edges of that cluster: the operation being sized, the people being scheduled, the two inputs feeding the formula, and the target it solves for.
- 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
Six questions come up in nearly every planning conversation about Erlang models, from the split between the three variants to how often a forecast needs rebuilding. Short answers below, in the order planners usually ask them.
What is the difference between Erlang B and Erlang C?
Erlang B assumes callers who meet a busy signal disappear and never call back, so it sizes trunks and lines. Erlang C assumes those callers wait in queue, so it sizes agent headcount. Most planning teams run both.
Who invented the Erlang formulas?
Danish mathematician Agner Krarup Erlang 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. The standard Erlang unit reference still credits that paper.
Is Erlang C still accurate for modern contact centers?
Erlang C is still the default in workforce management suites, but it assumes infinite caller patience. For chat and short message service (SMS), where callers abandon fast, planners layer Erlang A on top, as Call Centre Helper’s Erlang C guide explains.
What service level does Erlang C target?
The industry-default target is 80/20: 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.
How often should forecasts be refreshed?
Most mature BPOs reforecast in fifteen or thirty-minute intervals intraday and rebuild the base forecast weekly.
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