I cycle to work in an office with a single shower. When the shower is occupied I set my stopwatch for 10 minutes. When the stopwatch expires I trek back to the shower and try again. Sometimes it is occupied again.
What is the optimum time to set my stopwatch to minimise the number of return trips?
I chose 10 minutes because I guessed that that's probably how long a reasonably quick shower takes. But thinking about it perhaps a shorter delay might avoid me being beaten once the shower becomes free, whilst a longer delay would increase the likelihood that the initial occupier has left.
I realize there are loads of variables here that you might need to know so here's some details to get started with:
- All shower users use the same system when they arrive at work
- Shower users arrive at work at different times, but let's say between 9-10
- All shower users want to be out of their Lycra by the end of the morning (12) and to avoid interference with the lunchtime shower users. Their co-workers want them out of their Lycra ASAP. I'm not sure how to balance this requirement with the requirement to minimize the number of trips to the shower. Suggestions?
- Shower users take between 8 and 16 minutes to shower
- There are between 4 and 10 shower users on a given day.
- I realize there are better ways to organize the shower queue!
- All shower user use the same retry delay