How to project the service levels using Erlang A?

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How to project the service levels using Erlang A?
How to create a model which can help us in projecting the service levels using Erlang A?
For that, first of all calculate the no of agents required using Erlang A (including abandons), then also know about conversion from agents to no of contacts (using Erlang A) which can help us in projecting the service levels better?

Editor

Call Centre Helper

The Erlang Calculator uses a hybrid model
Our Erlang calculator uses a hydrid model. It uses Erlang C for getting staffing levels and Erlang A for the call abandons. I did look at using Erlang A for both but Erlang A has a tendancy to understaff, which is already a big problem in contact centres.

https://www.callcentrehelper.com/tools/erlang-calculator/
To use the Erlang A part you just need to press "Show Advanced Options" and then you need to enter an Average Patience. (In essence this is the Average Time to Abandon). The default time is 60 seconds.
You can plot out your abandon times to get this figure. More details in this article.
https://www.callcentrehelper.com/how-to-bring-down-your-call-abandon-rates-50805.htm

Efficiently using Erlang A
To use Erlang A, a new metric has been defined - average patience time which uses the data to predict the no of agents. But, the erlang calculator that you have created does not change the no of agents on changing the average patience time. Is this a bug? or the agents does not depend on the average patience time.
Can you share the logic how you are using the average patience time to predict the no of agents?

Erlang A
Anyone having idea behind the logic for Erlang A to calculate the no of agents required.

Editor

Call Centre Helper

This paper contains the formula
This paper contains the formula

https://arxiv.org/abs/1712.08445

I'm afraid though that the maths is non-trivial. It took months to figure out how it worked, and even longer to make it scalable.

Editor

Call Centre Helper

An article on the Erlang A Formula

Erlang A Article Question
The only part of the formula I do not understand is the bottom left hand part of the equation. I know that the load per server, servers, service rate, offered calls, and patience. What I do not understand is how this portion is worked out, is this a GCD of xxx? What is the A?

Editor

Call Centre Helper

A is normally traffic intensity
A is normally the traffic intensity - the length of time that all of the phone calls would take if ordered end to end.

This paper contains the formula
https://arxiv.org/abs/1712.08445
I'm afraid though that the maths is non-trivial. It took months to figure out how it worked, and even longer to make it scalable.

Editor

Call Centre Helper

Also helps if you follow the Erlang C formula

Erlang A Article Question
Well considering the majority of the WFM community uses excel for planning or providing quick answers to management it would be extremely helpful if Erlang A could be put into an excel format (w/ erlang c sheet the site provides).

By the way I did read about 3 different papers on Erlang A and I now understand that:

A = ((X*EXP(Y))/(Y^X))*EXP(GAMMALN(Y))*GAMMADIST(X,Y,1,1)

X = AHT*Agents / Patience
Y = Offered Contacts / Patience

The EXP(GAMMALN(Y))*GAMMADIST(X,Y,1,1) portion is a lower incomplete gamma function equivalent for excel without a script. I know I am not the only one asking for this to be added into excel.

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