Vinay Vasudevan

# The Mechanics of Erlang - ASA Model

Updated: Feb 7, 2022

It's time for another mathematical talk!!

A couple of weeks back, I had explained the mathematical formula of Erlang and how it works.

But that was for Service Level Models, and now we will see how the same would work for the Average Speed to Answer (ASA) Model.

The ASA model also works pretty much the same as Service Level (SL).

In the SL model, we found out what FTE is required to meet the target SL while here we are applying a similar method only this time find out the requirements to meet the Average Speed to Answer (ASA)

As I did earlier, this blog also has the calculated excel file attached in the end. Please check the file to understand more

We always thought that FTE is the result of all the parameters we provide, but ironically, the probable wait time is the actual output used to calculate other parameters.

FTE is only used as a trial and error to find out the requirement to meet the SL or ASA Target

**But, what is this probable wait time actually?**

**Is it Customer Patience Time? Or anything else**?

To understand this, let's take a deeper look into the Erlang Formulas

We know that a Danish mathematician named Agner Krarup Erlang formulated this method.

He initially formulated Erlang B, which worked fine until people found out that this method doesn't have options for customers to wait in the queue for someone to pickup the call.

Thus the need for another formula that essentially does all the functions as Erlang B and has the option for customers to hold on in the queue.

The **Erlang C** was born!!

This essentially means there must be some formula modification done to Erlang B to achieve Erlang C

Let's see what it was

Below is the formula for Erlang B

Below is the formula of Probable wait time, which is a part of Erlang C and was also used in my previous blog

In both these formulas, some alphabets represent the same meaning, like

E=A

N=m

Two difference between both formulas is the addition of component N/(N-A) and the summation till N-1 in the Erlang C.

Those two changes essentially provided the leverage for a customer to wait on the queue instead of disconnecting

I guess the mind is ringing a bell now, isn't it?

Well, there must be some logic used to get those modifications.

I'll leave it to the readers to research more on it.

**Limitations of Erlang B & C**

Erlang works on a specific set of assumptions that fail to work during times of high congestion. This is also termed a "high-loss system".

Erlang B doesn't account for queue waiting, but Erlang C overcame this problem.

However, Erlang C doesn't account for any Abandon %, due to which the staffing requirement is always on the higher side.

This problem is solved in Erlang X, which has fascinating formulas and methodology.

Hopefully, I'll get a chance to talk about Erlang X at some point.

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