Traffic Flow

[marcmagus]

Consider a mixed-sex set of people who occupy the same space for an extended period of time. Assume there are three restrooms attached to the space, one labeled Men, one Women, and one Men/Women. Each can accomodate a single person at a time. Assume that all the people involved obey the restrictions, and that everybody involved has a non-ambiguous identity of either Male or Female.

If you are going to occupy a bathroom for a relatively long time, should you use the single-sex bathroom for your own sex, or the mixed-sex bathroom? Your goal is to minimize the impact on the other occupants of the space in terms of their ability to use a bathroom with minimal wait.

Feel free to make the simplifying assumptions that the sex mix is approximately even and that there isn't a sex bias to frequency or duration of visits to the bathroom. Also feel free to assume that people will preferentially use their single-sex bathroom if it is available, and go to the mixed-sex bathroom only as an "overflow". Do these assumptions change your results? Can you get a more favorable result by relaxing them (changing the behavior of the other people)?

Yes, I think about these things...

Tangent: Why do we specify gender on single-person bathrooms, anyway? I can accept cultural mores against people of different sex being in the same bathroom at the same time, but I can't see what possible use there is when the occupancy limit is one.

Comments

[soulchanger.livejournal.com]

My intuition tells me that each person should use the single room, only using the mixed room as overflow. After some charts (resembling truth tables, since I used 1 to signify occupation, and 0 to signify availability) my intuition seems to be confirmed.