Unlocking the Power of Queuing Theory for FTE Calculations

Most WFM professionals have heard of Erlang C and most swear by it to calculate the staffing requirements for everything from multi-skilled voice to chat (more on that in a later blog).

Erlang distribution is particularly useful for modeling the arrival and service processes in queuing systems.

The Erlang-C formula accounts for the waiting time of a call and provides a means to calculate the probability of a call being delayed.

These approximations are highly beneficial in capacity planning, helping organizations allocate resources effectively and maintain efficient service levels.

But most WFM practitioners do not understand the underlying Queuing Theory which provides a valuable framework for analyzing and optimizing the flow of entities in various systems, ranging from call centers to computer networks.

We will look at using a simple approximation from this fundamental theory to make our lives easier.

Some WFM humor – Murphy’ Laws on reliability & queueing

  • If anything can go wrong, it will.
  • If you change queues, the one you have left will start to move faster than the one you are in now.
  • Your queue always goes the slowest.
  • Whatever queue you join, no matter how short it looks, it will always take the longest for you to get served.
% Difference between Queuing Theory Approximation & Erlang C results vs Service Time

What if complex macros or intricate math aren’t at your disposal?

The simplest formula to estimate the FTE required based on Service Level SL is as below –

Workload = Volume x AHT / 1800

FTE @ SL = Workload + SL x √Workload

Sample calculation to estimate FTE for 100 calls in 30 min with 600 sec AHT at 80% SL with 20 second service time –

Workload = 100 x 600 /1800 = 33.33

FTE = 33.33 + 80% x square root (33.33)

FTE = 33.33 + 80% x 5.77 = ~38

While using Erlang C and the fractional agents’ formulae the outcome is ~39. That is just a 3% variance, while the difference drops to 0.02% if we use a 10x workload (1000 calls every 30 minutes).  You can download the file for comparison here.

As with any approximation, there is a sweet spot, high volumes & medium to low service times will give you the most accurate results – see the graph above. But even with the edge cases – very low volumes and 180-second service time, the variance does not usually cross the 5% threshold.

Conclusion: While approximations have their nuances, they consistently hold their ground, serving as invaluable tools in the arsenal of a proficient WFM practitioner.

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