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

[petiteamazon.livejournal.com]

Tough call. As early as high school, I got used to using the single-person bathrooms interchangeably (although it's still kind of funny to come out of the men's bathroom and spot a guy coming out of the women's bathroom).

Great example of how it makes no sense to have gender designations for single-person bathrooms: at work, there are two single-person staff bathrooms, one designated male and one female. No problem, right? Uhm, there's only one male staff member. Essentially, he has his own bathroom, which most likely goes unused when he's not there. If I needed the bathroom and so did one of the ladies, I would feel perfectly comfortable using the men's I mean Ken's bathroom, although the other women would probably be weirded out by it.