July 21, 2022

How to use Erlang C to effectively plan call center staffing

Ryan Wang
Co-founder and CEO

Making sure you have the right number of support agents to quickly and reliably help customers is a critical component of workforce management. As a support leader, you need to consider the number of agents you have at your disposal, the number of customers you serve on a daily basis, and the average time it takes agents to respond to customer queries. 

One of the best ways to effectively plan your call center staffing needs is to use the Erlang C formula, a technique almost as old as telephones themselves.

What is Erlang C?

The Erlang C formula is one of my favorite sources of call center trivia. Conceived by Danish mathematician Agner Erlang in 1917, Erlang C is a capacity planning tool that allows workforce managers to identify their staffing needs by plugging in the number of agents they have at their disposal, their support center’s call volume, and the average response time of their operation. 

erlang c
Agner Krarup Erlang (1878–1929) pioneered queueing theory and was perhaps the first workforce manager.

Erlang C was originally designed to model the number of switch operators needed to operate the burgeoning telephone system. Fast forward to now, and we’re still reaping the fruits of Agner's mathematical insight, with call centers and support teams commonly using the same model, with slight modifications, to forecast staffing requirements.

Using Erlang C to make sure you have the right number of agents to quickly answer calls can mean the difference between success and failure. Need proof? An Arise survey found that nearly two-thirds of respondents will give up and abandon their call after just two minutes.

Why is Erlang C useful?

At its core, Erlang C allows you to model the relationship between staffing, call volume, and response time. These are factors that good support managers understand intuitively, but a little math goes a long way toward quantifying those intuitions.

Most often, Erlang C is used to estimate required staffing for a given target response time and expected amount of contact volume. For more on how to estimate the latter, see our blog post on how to forecast for customer support. Many online Erlang C calculators also factor in variables like shrinkage, occupancy, and concurrency. These additions make the formula flexible enough to model modern real-time channels like chat, SMS, and social media in addition to phone calls.

Note that in this post, we focus on staffing real-time channels. Erlang C is typically not appropriate for modeling channels like email, where response times may be in the hours or days and a backlog of tickets can build up over time.

How do you actually use Erlang C to plan staffing?

As discussed above, there are many calculators on the web that allow you to conduct Erlang C analysis manually. Rather than go deep into the details of how Erlang C actually works, we'll focus on how to interpret its results and use it to plan staffing.

Here are a few example calculations and how to interpret them. In the table below, the cells on the left represent inputs and the cells on the right represent calculations from Erlang. 

For example, if you receive 50 contacts per hour, contacts take 5 minutes to handle on average, and your goal is to respond to 90% of customers within 1 minute, then you'll need 10 people staffed in that hour and on average 60% of their time will be occupied with contacts. Note that we assume 30% shrinkage, which is the industry average — this metric captures the portion of time spent on breaks, meetings, or any activities that don't involve directly handling customer contacts.

Here are a few other takeaways from the table:

  • The value of scale really stands out. All else equal, baseline occupancy is much higher for a team receiving 150 contacts versus 50 contacts an hour. As a result, we often see teams with fewer than 20 people staff multiple channels at once or fall back to project-based and back-office tasks during downtime.
  • Reducing handle time has a big effect on reducing required staffing. As such, investments in tools and training that help the team solve customer issues more quickly are worthwhile. All that said, it's important not to single-mindedly optimize on speed, as both the customer experience and agent experience might suffer as a result.
  • Improving response time requires a proportionally larger increase in staffing at a larger versus smaller team size. That is, it gets harder to respond quickly to customers as you grow. There are many ways to interpret this, but our optimistic view is that small teams can and should build a culture of excellence driven by metrics before they start to find themselves grappling with the challenges of scale.

Determining the right inputs

If this all seems like it’s based on a lot of assumptions and fluctuating variables, that's because there are indeed many factors to take into account. We suggest setting aside time to do research on industry averages for measures like shrinkage and occupancy, which are well studied. For other variables such as target response time, what makes sense for you will depend a lot on the characteristics and goals of your business — this is where judgment and tradeoffs come into play. 

Finally, metrics like handle time and forecasted volume are fairly science-driven. In these cases, you'll need to consult your analytics  and/or your data team to dive in.

As with any quantitative model, the Erlang C formula is only as accurate as its assumptions, and so you absolutely do need to work off the right data in order to make the right decisions. As a brief illustration, we'll work off the same inputs as above (90% of responses within 60 seconds). If forecasts are off by 25%, you could find yourself understaffed or overstaffed by several people.

  • 35 contacts → 8.5 agents at 49% occupancy
  • 65 contacts → 13 agents at 60% occupancy

Making the hard decisions

At the end of the day, support teams need to make a number of hard decisions in order to balance serving customers promptly while maintaining economic viability. Erlang C analysis removes some of the guesswork by clarifying how staffing decisions impact bottom-line customer-facing outcomes such as response time and service level. However, as we've shown, getting this right also requires having access to good data and projections.

If you need help with making sure your inputs are solid, Assembled combines in-depth industry knowledge with seamless integrations for Zendesk, Kustomer, and Intercom to pull the most accurate data. Please get in touch to learn more.

This blog post was originally published on May 21, 2020. It was updated on July 21, 2022.

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