# How many inbound agents do I need? The Erlang C formula will tell me …… right?

October 25, 2013 Stu Harris

Not exactly.  It does have its shortcomings.  The Erlang C formula is named for its creator, A.K. Erlang, a Danish mathematician who first published it in 1917.  It’s been used by call centers for staffing prediction ever since there were call centers.

As most call center managers know, the inputs to the formula are: 1) the number of calls expected to arrive in a given time period; 2) the average length of the calls and any after call or wrap-up time; and 3) a desired level of service expressed as the percent of calls to be answered in a given number of seconds.  The formula can then give you the best number of agents to use to meet the desired service level.

However the word “best” is very relative here.  What most managers don’t realize is that the Erlang C formula ignores or distorts certain realities concerning the arrival and handling of inbound calls.  For example:

1.  It assumes all callers have infinite patience and will never hang up (abandon) from queue.  Clearly, callers are not so patient and will hang up in queue and this is a basic management issue for call centers.

2.  It assumes all the calls start and end within the time period.  Obviously, if you are looking at a 15 minute period and have a 5 minute average call length, then a high percentage of the calls being handled in the time period will have arrived in the previous time period, or will end in the next time period.

3.  It has a wrong assumption about average talk time.  You might think that the probability of how long a call is likely to last would follow a bell-curved shape graph with the average in the middle.  Actually it doesn’t.  If you were to plot all the call lengths over a period of time on a graph you’d get a ski slope shaped graph:  Lot’s of calls being handled quickly, and a few calls taking a very long time.  How steep the slope is depends on what service your call center provides.

4.  In addition to ignoring caller abandonment from queue, the Erlang C formula doesn’t take into account caller re-try.  When callers do abandon from queue, a certain percentage of them will call back again trying to get an agent, and on average they will wait a certain amount of time before doing so.  If you have a lot of abandonment, you’ll have a lot of caller re-try.  This adds to the number of calls you originally thought you’d get.

Without going into the math, the upshot is that the Erlang C formula will most likely over-staff you:  it will tell you to use more agent that you actually need in reality.

So what to do?  Another formula?  No, simulation….  I’ll cover this in an upcoming post.

In the meantime take a look at this paper I wrote:  A Primer on Call Center Staffing Methods.

Every call center manager’s old friend, Agner Krarup Erlang