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It can't be that complicated.

My doctor's office phone manages "You are number two in the queue". Somewhere, maybe it was a previous doctor, added "and should expect to wait about 5 minutes".

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Even in my internal company tech support line they play that "higher than expected call volumes" message, but their website also has counter on it that tells you just how many people are on hold and even when it is just one (me) it plays that message.
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The only ones I believe are the ones that tell you the estimated wait time or number ahead of you (most of which offer to call you back).

It is funny to hear "our wait times are higher than average, your wait is estimated to be zero minutes".

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Easy for that to be true: just set your expectations to zero.
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All call centers are actually located in Lake Wobegon, where all the call wait times are above average.

( https://en.wikipedia.org/wiki/Lake_Wobegon#Recurring_monolog... , for the probably many people who don't know the reference.)

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