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

[miintikwa.livejournal.com]

If I knew that I was going to be in the potty room for a while, where a while > than normal bathroom time, I would probably elect to use the mixed gender room, out of politeness's sake.

[marcmagus]

Yes, but why is that the more polite decision? Do you agree with me that polite = minimal average time other people spend waiting to get into a bathroom or are you using a politeness which = minimal chance that someone will have to use their second choice of bathroom? Or do you have some other basis for politeness?

If you agree with me, why does using the mixed-sex room lead to the desirable outcome? (My intuition agrees, but I haven't succeeded in backing it up with anything remotely resembling a proof yet; nor even a good persuasive argument.)

[miintikwa.livejournal.com]

For me, politeness = minimizing the chance that someone else would have to use their 2nd choice bathroom.

And the arguement that I use is my mother. This will probably sound silly, but here goes.

If *I* use the mixed sex bathroom, which might make someone of an elder generation uncomfortable, there is less chance that the elder person will be confronted with that choice. Now, granted, you were not stating that a person of the elder generation was there- but that's the basis for my choice.

If I were at a party with my Mom, I'd use the mixed sex bathroom so the regular bathroom was open for her.

See?

[kiddens.livejournal.com]

Written from the perspective of a man and using your assumptions about equal demand and duration:

Regardless of which bathroom I choose, we can simultaneously also satisfy the demand of one woman - so remove the lady's room from the equation.

If I use the men's room, we can satisfy additional demand of one person regardless of gender. If I use the neutral room, we can only satisfy the demand of an additional man. Therefore the gender neutral bathroom is preferable for demand satisfaction.

If you can't use the assumptions about equal demand and duration, then the problem changes. You need to know something about the distribution of requests and the service times and the problem becomes much harder since it may become more favorable to leave the option for two females rather than be able to serve either gender.

[kiddens.livejournal.com]

Whoops, I meant the men's room is better. I had the logic all in my head and got the label wrong.

[marcmagus]

Yes, but consider the high-demand situation.

Hmmm...I had this whole write-up about how the women's queue would move at 3x the rate of the men's queue in the situation that the men's room is occupied. Halfway through I realized I was wrong: if you assume a single queue which dispatches the frontmost person permitted to use a room as it becomes available, you'll briefly see higher throughput of women. Then the queue will become stacked at the front with men, and the mixed-sex room will become a de-facto men's room if the distribution is roughly equal.

If you occupy the mixed-sex room, queues move normally at reduced capacity.

So it's pretty much irrelevant which room you occupy if there's a lot of contention for the resources (assuming a queuing behavior rather than a mob . . . if someone random is selected as each room becomes available, then occupying the men's room creates a preferential situation for women in line over men--again assuming high contention for the shared resources). If it mattered it's an interesting question: are we optimizing for average wait (in which case it doesn't matter) or for worst expected wait (in which case it does) or for something else?

Another thought: if we assume demand and duration are equal (or don't show a sex bias), but allow for the possibility that another person will have an unusually high duration, it's preferable to choose the single-sex room. If you occupy the mixed-sex room and any other person enters for a long duration, one gender will block until one of you finishes. If you occupy the single-sex room, there are two possibilities, roughly equally weighted: someone of your sex enters for a long duration, and your sex blocks until one of you finishes or someone of the opposite sex enters for a long duration, and everybody can use the remaining room with reduced capacity.

I'm trying to think of a situation in which the optimal choice is to occupy the mixed-sex room. I thought I had one, but, as stated, I was wrong.

[marcmagus]

Your mom would be uncomfortable using a bathroom which might be used, before or after—but not while—she uses it, by a man? That's fascinating, since I'm quite certain that's not the case in the absence of any markings upon the door (think of homes). I wonder what it is about making it explicit that the bathroom is for both sexes would cause discomfort with it?

[miintikwa.livejournal.com]

I don't know that she would be- I'm just saying that there is a chance that it might make her uncomfortable, and I would rather remove that chance.

[mneme]

You should use the single-sex bathroom. The mixed BR takes all comers, and so is more needed; in the degenerate case where you are M and only F's need the restroom, the throughput of the bathrooms is twice as high if you take the M-only room vs the mixed one. There is no degenerate case where there's an impact on throughput by taking the single-sex bathroom, unless customers choose not to use a BR at all rather than using the mixed-sex BR.

I prefer that single-person bathrooms be genderless myself -- it makes much more sense, especially when women tend to need more bathroom space per person.

(and will happily ignore the gendered signs on most single-occupancy bathrooms as needed).

[pixel.livejournal.com]

I think single-occupancy bathrooms have gender labels in most places for the same reason that elevators for two-story buildings have floor buttons. Consistency. The less change from the expected the less chance for confusion and therefore less backup caused by confused users.

Though this is also very user-group dependent. Someplace like the Diesel cafe will have very different user expectations then, say, a family restaurant in Southie.

[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.

[illogicalvulcan.livejournal.com]

I'm not going to argue a position now, because it's late, but my choice would be affected by what I was using the bathroom for. If I were just heading off to pee, I'd use the bathroom furthest from the entrance. (My preference. No one else need do this.) However, if I were...um...taking care of female things, I would wait for the women's room to be available. This avoids the risk of wigging out some 11 year old boy, and the risk of some jackass making crass sexist remarks.

[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.