What happens when you add a new teller? (2008)
johndcook.com
johndcook.com
1: https://www.nytimes.com/2007/06/23/business/23checkout.html
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.
(Not the application to retail management, which is straightforward, but the application to getting a better job.)
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.
The article mentions that as one of the two problems: "If customer arrivals were exactly evenly spaced and each took exactly 10 minutes to serve, there would be no problem."
"It's also why so many businesses use a single queue with multiple tellers/ cashiers."
The article implicitly assumes a single queue. But, as long as any empty queue is immediately filled by someone switching from another queue, this assumption doesn't affect the expected total # of people waiting.
[1] To put it another way, you can assume entrants plan for the line to take less than the 95th (or whatever) percentile time; the lower you get this figure, they better they can allocate their time for other tasks.
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
If you had them as self-contained shower rooms with changing area, that would probably be better from a personal standpoint and also alleviate the issue you raised.
Not the OP though, so who knows.
The restrooms have single line of stalls. There's a moveable wall between the stalls to change the allocation of how many men's stalls there are versus women's. That makes it so if you're running an event that tends to attract more people of one gender than the other, you can create more toilets for that gender. Quilting expo? More women's stalls. PC gaming event? More men's.
Likewise you'll serve half your customers within X minutes. Half the remainder within 2X, half the remainder within 3X etc.