
What happens when you add a new teller? (2008) - behoove
https://www.johndcook.com/blog/2008/10/21/what-happens-when-you-add-a-new-teller/
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tjpaudio
Kind of a textbook description of queue theory if you were taking a stochastic
processes class. If the author really is suggesting this for use in retail
line situations, he is out of touch because... retail managers have no idea
what queue theory is. If they did, they would be making much more money, and
not working in retail. Staffing is more of a function of how many people you
can get on the clock without getting yelled at by regional managers (who also
do not know queue theory) for overstaffing.

~~~
Spooky23
That’s not true at all! A good GM understands throughput and may get bonuses
based on that.

The retailer I worked at in the 90s also tracked the ring rate and time per
customer for cashiers, and made scheduling and hour decisions based on
performance.

~~~
tjpaudio
Thats great and all, but also not queue theory.

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Animats
This is classic open-loop queuing theory with Poisson arrivals. Nothing really
works like that. There's always a "rejection rate", where people leave the
line before being serviced. Or, in networking, the connection times out. Or,
for a shopping site or a real store, you get an "abandoned cart". In real
life, this has a lot to do with how many sales you lose.

In the early days of the Internet, people were trying to analyze datagram
networks as open-loop systems with Poisson arrivals. That's because everybody
read Kleinrock back then. His thesis was on Western Union Plan 55-A, which was
Sendmail made out of telephone relays and paper tape punches feeding paper
tape readers as buffers. A mail system behaves much more like an open loop
system - people don't mail less as the mail propagation time goes up. That was
the wrong model for IP messages, because TCP connections add a closed loop
system on top of IP.

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ogre_codes
Seems to me the big problem with any kind of retail queue is highly
inconsistent service times. If you have a consistent time/ customer, it's easy
to predict. As soon as you have some customers taking 20 minutes and some
taking 2 minutes all the simple math goes out the window. This is why some
people get so infuriated when they see the person in the front of the line
break out a fist full of coupons, food stamps, or wants to pay with a check.
It's also why so many businesses use a single queue with multiple tellers/
cashiers.

~~~
dreamcompiler
This happens a lot in retail, the DMV, post office, etc. The best way to model
it is with a meta-process where servers randomly disappear and reappear. This
also captures the infuriating phenomenon of tellers going on break or (worse)
looking like they're available when they're not because they have to stop and
count the till or something.

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mynameishere
It's all fun and games until it's not a bank with one teller, but a LabCorp
with one phlebotomist, and you're not there to give a blood sample, but a
urine sample.

~~~
walshemj
Or you get some one like me with uncommon tests I once had 75% of my local
hospitals phlebotomist's working out how to do this particular test.

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elchief
Did a fun project for my MBA. A bike parking facility downtown, where you can
park your bike securely, showers, lockers, towel service, ironing boards, buy
some coffee and a snack. Raised $80k for it...needed 100. Anyways

We modeled the showering process. Had some data on how long people took to
shower. Needed something like 3 showers per gender to get good throughput

One of the MBA profs didn't like this for some reason. Didn't believe it would
be enough (without any numbers to back it up). We were like, well if we add a
fourth shower we can accommodate dozens of more people. He liked that even
less

~~~
davinic
Why gender the showers in the first place? Seems like added complication for
little to no benefit by splitting into separate queues.

~~~
elchief
we did a survey of cyclists and gendered bathrooms were much preferred. this
was 9 years ago though...

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talaketu
Community consultation is the right thing to do! I wonder if modelling might
have predicted better service times for the majority gender with non-gendered
bathrooms, and that might have swung the survey result.

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dang
A thread from 2015:
[https://news.ycombinator.com/item?id=9652882](https://news.ycombinator.com/item?id=9652882)

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crystaln
Why I will never live anywhere with roommates, or have an event, anywhere with
one bathroom!

~~~
RealityVoid
Meh, it's not that bad. I lived my 6 years of college in a dorm with 5 people
lodged in one room - 15ish m2. One bathroom in each two room duplex containing
two sinks, one private toilet and one private shower. Surprisingly, it worked
really well. We rarely had to que and if someone was using a part of the
bathroom you could still use the rest of the facilities.

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jph
The teller post and queueing theory ideas are included here:
[https://github.com/joelparkerhenderson/queueing_theory](https://github.com/joelparkerhenderson/queueing_theory)

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wodenokoto
What does it mean that service times are exponential?

~~~
yaks_hairbrush
Good question! It means that the probably of finishing in the next increment
of time is always the same. Just got up to the teller? There's, say, a 20%
chance that you're done within the next minute. Been at the teller's desk for
30 minutes already? Still a 20% chance that you're going to be wrapped up in
the next minute.

~~~
sopooneo
This might be saying the same thing in a slightly different way. But does it
also mean that if we plot "service times" on the X axis and frequency on the
Y, then in the first quadrant we get something high on the left, getting lower
as it goes right, and asymptotically approaching zero as it goes to infinity
on the right?

