The Formula at the Heart of CX: Calculating Erlang C

What is Erlang C?

Developed in 1917 by Danish mathematician A. K. Erlang, Erlang C is a formula for calculating the number of contact center agents needed to answer a given number of calls in order to achieve a particular service level. In short, how many agents you need to cope with demand within the boundaries set by your SLAs.

The formula results in a probability (Pw) that a given call will have to wait in a queue, given the traffic intensity (A) and the number of available agents (N). Originally developed to calculate wait times in telephone exchanges, the mathematics still holds up (with some exceptions) to the modern-day contact center.

Put simply, understanding Erlang-C will help you schedule the right number of agents to meet a given level of demand. This allows you to:

• Effectively schedule agents in advance, supporting flexibility for agents whilst factoring in their preferences and holidays.

• Minimize wait times for customers, reducing frustrations and delivering delightful experiences.

• Balance costs to create outstanding customer experiences without breaking the bank.

Now that we’ve established the benefits of the Erlang-C formula, how do we set about calculating it?

Calculating the Erlang-C Formula

To get an answer (Pw) out of the Erlang-C formula, we need to prepare a couple of inputs. Those are A (traffic intensity) and N (number of available agents). Both are separate values we need to calculate.

Calculating Traffic Intensity

‘Traffic intensity’ refers to the length of time taken up by all incoming calls, added together. That means if the average length of a call is around three minutes, and you receive one hundred calls within a given period, the traffic intensity of that given period would be 3 minutes x 100 = 300 call minutes.

Dividing the call minutes by 60 would yield a value for Call Hours, also known as Erlangs. In this case, we would end up with 5 Erlangs (Call Hours).

Calculating Agents Required

Next, we need an estimate for the number of agents required to meet that intensity of traffic.

We should assume within an hour, one agent can handle one Call Hour of traffic. This assumes that every call comes in one after another, with no time spent in queues. In our example, this means we need 5 agents. But, the number of agents could be more or less than this ideal number.

The result: Pw

Inputting these two values into the formula (Don’t worry about the complex mathematics just yet) will yield a percentage result. This number represents the percentage chance that a call, made at any point within the given time period, will have to wait before an agent picks up the phone.

Service Levels from Erlang-C

Once we have a Pw value, we can use another formula to calculate service levels

From the result of this formula, you can tell whether your contact center is going to meet its SLAs for a given level of demand and a given number of agents.

Tools for Calculating Erlang-C

Erlang-C is incredibly complex. Even when you understand the mathematics behind the formula, calculating each outcome for different values of A and N would take a huge amount of time. The best way to approach Erlang-C is through an automatic scheduling assistant, allowing you to input the basic values, in order to calculate service levels without the need for manual math.

 Such a solution would offer:

• Automatic scheduling, leveraging the Erlang-C formula to calculate the minimum number of agents required at a given time of day to meet agreed SLAs.

• Predictive demand, using historic data on contact demand levels to calculate levels of demand as accurately as possible to support Erlang-C calculations.

• Flexible reports, combining Erlang-C and predicted Service Levels with other metrics of customer experience quality, for a complete overview of contact center performance.

Moving Beyond Erlang-C

Erlang-C is an essential mathematical tool for supporting the operation of the contact center. When it comes to scheduling the right number of agents to meet demand, you simply can’t do without it. But Erlang-C doesn’t offer anything more than that. To really drill down into contact center performance, you need to be tracking a host of different metrics:

• Customer Satisfaction (CSAT) - Customer satisfaction begins with a simple question, ‘How satisfied are you with your experience?’ From here, customers respond on a scale from ‘very dissatisfied’ to ‘very satisfied’. These results fall on a scale of 1 to 10, from which you can calculate an average score across various populations, anywhere between 1 and 100.

• Net Promoter Score (NPS) – Net Promoter Score doesn’t just measure customer satisfaction, it measures customer advocacy. By asking which customers are likely to recommend your business, it serves as an effective indicator of which customers are likely to stick by your side in the long run.

• Value Enhancement Score (VES) – A relatively new metric, VES asks two questions, ‘How successfully were you able to use our product/service?’, and, ‘How confident are you with your purchase?’ In answering these questions, the customer gives their opinion on both your business and the impression conveyed by your customer service.

• Customer Effort Score (CES) – CES measures how much effort a customer had to put in to reach a solution to their problem. Friction within your customer service estate, confusion on the part of agents, or a failure to resolve a problem all lead to poor Customer Effort Score.

Each of these metrics provides insight into different aspects of your contact center performance. Ideally, your customer contact should be both efficient and high quality. Reaching this high standard is a different matter entirely.