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 -

	Erlang C	Erlang calculators for call centers, help desks, checkout queues, where customers can wait in a queue. cc-Modeler Lite and cc-Modeler Professional use Erlang C calculations.
	Extended Erlang B	Used by telephone system designers to estimate the number of lines required for PSTN connections and takes into account the additional traffic load caused by blocked callers immediately trying to call again if their calls are blocked.
	Erlang B	Estimates the number of lines required for PSTN connections (CO trunks) or private wire connections.
	Engset	Used to explore the relationship between the traffic offered to a trunk group, the blocking that will be experienced and the number of lines provided when there are a finite number of sources from which the traffic is generated. It is more accurate than Erlang B, which tends to over-estimate blocking.

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 -

	Calls are offered randomly in a queue (Poisson arrivals)
	Users wait if they find the system busy (no account is made of the effect of abandoned calls)
	Service times are exponential
	Users are served in the order of their arrival
	Users are directed to the first-available agent
	Queue sizes are unlimited
	There are not dramatic variations in call volumes within the period being calculated

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.