The ABC of Erlang

In the early twentieth century, three Erlang formulas were developed: Erlang A, Erlang B, and Erlang C. A Danish mathematician named AK Erlang invented Erlang B first.

In 1917, AK Erlang invented the Erlang C formula, followed by another mathematician, Conny Palm, in 1946, who invented the Erlang A formula.

While the Erlang B formula is no longer widely utilized in contact centers, Erlang C and Erlang A continue to play a significant role in contact center labor-management (WFM).

Additionally, “Erlangs” is a unit of measurement. More information about this metric may be found in our article: What exactly are Erlangs?

The Erlang B Equation

Originally, the Erlang B formula was used to determine the probability of a phone system being blocked. Thus, when contact centers were first established, Erlang B was used to determine the number of lines required for queuing in a contact center. Thus, when applied to the contact center, the inputs to Erlang B would include expected call volumes and Average Handle Time (AHT) to determine how quickly the queue would move on average. This figure would have an effect on the number of phone lines required.

The C Formula in Erlang

The Erlang C formula, which is based on the Erlang B formula, is used in the contact center to determine the number of advisers required to satisfy a specified service level. This is an old formula that is still widely used in the business.

The formula is encoded in devices known as “Erlang Calculators,” which simplify the process of calculating contact center manpower.

The Erlang Calculator does this by converting the number of calls, AHT, and service level into the number of workers necessary, while later versions additionally incorporate other variables such as occupancy, shrinkage, and average patience.

However, in order to determine average patience, you’re going to need some assistance from Erlang A.

Erlang’s Formula A

While the Erlang C formula was really useful, it overlooked the number of people who abandon their calls before reaching an adviser.

Fortunately, in 1946, Swedish mathematician Conny Palm proposed a modification to the Erlang C formula known as the Erlang A formula that does account for “Abandons.” Indeed, Erlang’s A stands for Abandons.