The Mechanics of Erlang – ASA Model

It’s time for another mathematical talk!!

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 are going to see how the same would work for Average Speed to Answer (ASA) Model.
For people who didn’t go through the Service Level (SL) Model. Here is the link
The ASA model also works pretty much the same like Service Level (SL). 
In the SL model, we found out what FTE is required to meet the target SL whilst here we are apply 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 resultant of all the parameters which we provide, but ironically Probable wait time is the actual output using which we 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 on the queue for someone to pickup the call
Thus the need for another formula which essentially does all the functions as Erlang B, but also 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 formula, some alphabets represent the same meaning, like
Two difference between both the formula is 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 certain set of assumptions which fails to work during the time of high congestion. This is also termed as “high-loss system”
Erlang B doesn’t account queue waiting, but Erlang C overcame this problem. 
However Erlang C doesn’t account for any Abandon % due to which the staffing requirement are always on the higher side.
This problem is solved in Erlang X which has very interesting formulas and methodology.
Hopefully I’ll get a chance to talk about Erlang X
There is an interesting blog written on Erlang X. Click on the below link to read that blog
Below is the link for excel working model

Thank you for the patience!!
Stay tuned for next Article????????

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