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.
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.
number of lines required for PSTN connections (CO trunks) or private
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
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 -
offered randomly in a queue (Poisson arrivals)
Users wait if
they find the system busy (no account is made of the effect of abandoned
served in the order of their arrival
directed to the first-available agent
Queue sizes are
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.