The Erlang-C Formula - An Introduction

Background about the widely-used Erlang-C formula.


Airline checkin

Erlang-C is the name of a mathematical formula widely used for telephone systems and call-centres. The formula applies also to many other queueing situations such as supermarket checkouts and airline check-in. Erlang-C is named after Agner Krarup Erlang, a Danish mathematician and engineer who developed his famous formula in 1917.

Supermarket checkouts

Although the Erlang-C formula can be used to calculate, for example, the number of call-center agents needed, or the number of checkouts that should be open, it can also be used to demonstrate a number of general principles about queueing.

Where customers (people, calls, things) form a single queue (or line) to be served by a group of agents or machines, we can use Erlang-C to tell us about the waiting times and queue size. There are some important assumptions, such as customers get served first-come first-served, there are enough agents to deal with the customers, and customers never give up waiting and leave. As long as these assumptions match the real situation reasonably well, Erlang-C is a very useful management tool.

Erlang developed several formulae, each for a different queueing situation. Erlang-C is the most well known and most widely used, but there are also Erlang-A and Erlang-B.

Many people find any sort of mathematical formula daunting. If you don't want to tackle the technical details of Erlang-C then you can use a software package such as Mitans T-Calc that lets you use Erlang-C and related formulae painlessly.