the erlang c traffic model
The Erlang traffic models were established by A.K. Erlang, a Danish scientist who is credited with much of the early work in telephone traffic design. He discovered the mathematics underlying queuing, a branch of statistics now termed 'queuing theory'.
'Erlang' calculators are used throughout the world to carry out a variety of statistical calculations associated with telecommunications systems and call centers.
There are several variants of Erlang calculator for specific purposes -
The Erlang C calculator models the performance of systems which incorporate queuing (rather than a caller simply getting a busy signal and hanging up). Queuing applications include switchboard operators, call center agents and helpdesks. However the same calculations also apply to supermarket checkout queues, toll booths etc.
The Erlang C model makes the following assumptions -
The actual formula for Erlang C calculations is -
where the result is the probability that a caller will not be answered immediately and will have to wait (i.e. be queued).
Other parameters can also be derived from this formula including the number of agents needed, the ASA, the service level (e.g. percent of calls answered within 40 seconds), number of calls queued etc.