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What is Erlang C?
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How Accurate is Erlang C?

Erlang C has been used for many years to calculate agent staffing needs in call centers. It is the 'industry standard' mathematical model and generally provides quite accurate results.

When using Erlang C though, it is important to understand that it has several underlying assumptions and also that the results do depend on the accuracy of the input parameters (the old 'garbage in - garbage out' rule). 

Overall, Erlang C provides slightly conservative results in practice (that is, it will slightly overestimate the actual agents required to meet a particular service level).


There are several underlying assumptions in the Erlang model which are not entirely borne out in most call center operations -

Assumption Notes

Callers wait on indefinitely in the ACD queue - they don't hang up

In real life some callers hang up, either immediately or after varying on-hold times. Some of them will retry later.

If the ADA (average delay before answer) is less than 1 to 2 minutes, this does not significantly affect the results.

Calls arrive randomly in a Poisson distribution

This means that there are no large spikes and troughs in the incoming call rate.

For a medium to high call rate, this assumption is generally satisfied over a 15 or 30 minute interval. 

For low call volumes however (e.g. a small help desk) there will be quite significant call fluctuations from interval to interval.  

The call center operates in a 'steady state'

The main aspect to this assumption is that there is no backlog of calls from previous intervals. In practice if there is an overload of calls at one time of the day, then some of the callers will actually be answered in the next interval.

For centers with reasonable service levels and medium or high call volumes this is not significant. 

For 'event driven' centers such as I.T. support, in the case of major problems or outages then there will be  occasional spikes and resulting backlogs. Erlang C does not cater for this.

That there are enough trunks  'Trunks' are the incoming phone lines. Most calculators assume that no more than 1% of callers will encounter a busy tone (i.e. there are enough trunks available for incoming calls plus the callers on hold).

Input Parameters

The input parameters to Erlang C calculations directly impact on the accuracy of the results.



Calls per hour

This is always answered calls, not offered calls. Ensure that the calls per hour is taken from a representative day of the week (and period in the month).

Talk Time

The total call duration is talk time plus wrapup time. (The total call duration is often called 'Average Handling Time' or AHT).

Talk Time can generally be taken directly from ACD reports. 

Wrapup Time

Wrapup Time is the second element of total call duration.

It is much more difficult to measure accurately -

  •  If you have 'call forcing' in effect on your ACD, then the wrapup time is simply the delay between an agent terminating one call and being offered the next call

  •  If you are not using call forcing, wrapup time is much more difficult to  establish. generally the numbers reported by an ACD are not accurate as they usually include such things as agent 'not ready', breaks etc. 

Sometimes it is only possible to estimate the wrapup time.

Service Level

The required Service Level, either expressed as -

  •  An Average Delay Before Answer (often also called 'Average Speed to Answer' or ASA) e.g. 20 seconds average delay; or

  •  Percent of calls answered within a threshold (e.g. 80% answered within 40 seconds). This is often also called a 'Service Objective' or SO).


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