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I am working on a project with a call center. Long story short, I am analzying the data revolved around the incoming calls to this call center in order to eventually use a queueing model. A queueing model is one which you provide with certain values such as the average service time of calls (average value of how long calls last) and some other inputs, and it would at the end of the day tell us how many agents need to be planned to answer incoming calls.

My question is: Should I insert the mean value or the median value of my service time data to this queueing model? (The data follows a lognormal distribution).

Note: 1- I cleaned my data from outliers so I suppose a mean and a median value are both usable. 2- The answer to my decision is probably going to be dependent on what my end-goal is, which is why I tried to explain my goal in the above paragraph.

Could someone shed some light on this? Thank you!

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    $\begingroup$ Since you are giving this queueing model multiple values, why not give it more than just the mean or just the median? Why not both? Why not some quantiles? $\endgroup$
    – user2974951
    Commented Mar 3, 2023 at 9:34

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The standard results in queuing theory predict mean wait times, so you will find means easier to work with.

But let me ask something. You say "I cleaned my data from outliers". Do you mean that you dropped the records of really long waits? That sounds like a mistake - those are the most important records for this application, aren't they.

You wouldn't invest based on a model that ignores stock market crashes.

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  • $\begingroup$ First of all, thanks for the quick reply ! By cleaning my data, I mean I used the Interquantile range method to remove outliers. So yes, in a way I dropped really long waiting times. A question I can ask here is: "Outliers" are values which are out of the norm and which occur rarely within the dataset, as far as I understand. Doesn't that mean we should remove them in such a study? $\endgroup$
    – Sam
    Commented Mar 2, 2023 at 16:29
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    $\begingroup$ No, actually. Outliers are merely data points that require some more investigation. If they are invalid (bad data, equipment, etc.), then by all means remove them. But otherwise, you should generally keep them in. Ask yourself why those outliers occurred: that might give you insight into your business question that you wouldn't otherwise have had! $\endgroup$
    – Adrian Keister
    Commented Mar 2, 2023 at 16:41
  • $\begingroup$ The data I have is recorded automatically and so I am almost sure there wouldn't be any "bad data" or equipment failor or something like that. I agree some extra investigation is needed to check the source of these "outliers", thank you for the help ! $\endgroup$
    – Sam
    Commented Mar 2, 2023 at 16:48
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    $\begingroup$ As a customer calling a call centre, I forget the ones where the call is answered immediately and the problem dealt with in 2 minutes. I often remember the ones where the calls dealt with a complicated problem and took 20 minutes. I always remember the one where the call was not answered for 40 minutes and then after 10 minutes I was told that the service agent had spent too long on my call and I was cut off because there were others waiting. $\endgroup$
    – Henry
    Commented Mar 2, 2023 at 18:44
  • $\begingroup$ @RichardHardy weight what? Are you telling me that it is incorrect? $\endgroup$
    – Sextus Empiricus
    Commented Mar 3, 2023 at 14:16

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