Editing Erlang (unit) (section)

== Calculating offered traffic ==

Offered traffic (in erlangs) is related to the ''call arrival rate'', ''λ'', and the ''average call-holding time'' (the average time of a phone call), ''h'', by:
: <math> E = \lambda h </math>
provided that ''h'' and ''λ'' are expressed using the same units of time (seconds and calls per second, or minutes and calls per minute).

The practical measurement of traffic is typically based on continuous observations over several days or weeks, during which the instantaneous traffic is recorded at regular, short intervals (such as every few seconds).  These measurements are then used to calculate a single result, most commonly the busy-hour traffic (in erlangs).  This is the average number of concurrent calls during a given one-hour period of the day, where that period is selected to give the highest result. (This result is called the time-consistent busy-hour traffic).  An alternative is to calculate a busy-hour traffic value separately for each day (which may correspond to slightly different times each day) and take the average of these values. This generally gives a slightly higher value than the time-consistent busy-hour value.

Where the existing busy-hour carried traffic, ''E''<sub>c</sub>, is measured on an already overloaded system, with a significant level of blocking, it is necessary to take account of the blocked calls in estimating the busy-hour offered traffic ''E''<sub>o</sub> (which is the traffic value to be used in the Erlang formulae). The offered traffic can be estimated by {{nowrap|1=''E''<sub>o</sub> = ''E''<sub>c</sub>/(1 &minus; ''P''<sub>b</sub>)}}.  For this purpose, where the system includes a means of counting blocked calls and successful calls, ''P''<sub>b</sub> can be estimated directly from the proportion of calls that are blocked.  Failing that, ''P''<sub>b</sub> can be estimated by using ''E''<sub>c</sub> in place of ''E''<sub>o</sub> in the Erlang formula and the resulting estimate of ''P''<sub>b</sub> can then be used in {{nowrap|1=''E''<sub>o</sub> = ''E''<sub>c</sub>/(1 &minus; ''P''<sub>b</sub>)}} to provide a first estimate of ''E''<sub>o</sub>.

Another method of estimating ''E''<sub>o</sub> in an overloaded system is to measure the busy-hour call arrival rate, ''λ'' (counting successful calls and blocked calls), and the average call-holding time (for successful calls), ''h'', and then estimate ''E''<sub>o</sub> using the formula {{nowrap|1=''E'' = ''λh''}}.

For a situation where the traffic to be handled is completely new traffic, the only choice is to try to model expected user behavior. For example, one could estimate active user population, ''N'', expected level of use, ''U'' (number of calls/transactions per user per day), busy-hour concentration factor, ''C'' (proportion of daily activity that will fall in the busy hour), and average holding time/service time, ''h'' (expressed in minutes).  A projection of busy-hour offered traffic would then be {{nowrap|1=''E''<sub>o</sub> = {{sfrac|''NUC''|60}}''h''&nbsp;erlangs}}.  (The division by 60 translates the busy-hour call/transaction arrival rate into a per-minute value, to match the units in which ''h'' is expressed.)