I am talking about a rectangular swimming pool.
In my country, we are allowed to swim in a direction parallel to the width of the pool when there are too many customers come. It is usually done automatically without any command by the swimming pool staff. In other words, it looks like a common consensus in my country.
Long story short, is this allowed in Japan? Do we need permission from other customers first?
Pools in Japan are usually divided in two sections: lanes running the length of the pool for "serious" swimmers, and a general section for everybody else (including children etc).
In the "serious" lanes, all you're allowed to do is swim up and down the lane at the same speed as others in that lane, which are typically physically marked with lane ropes. Here's what the Olympic 50m pool looks like at the Tokyo Metropolitan Gymnasium:
(publicity photo courtesy TMG)
In the "free for all" section (which for the TMG means the entire 25m pool) you can do anything you like, but you're unlikely to have much luck doing laps the width of the pool because of school lessons, teenagers horsing around, random pensioners doing their exercises, etc.
As a sidenote, beware that Japanese pools tend to have a pretty strictly enforced "dress code": this usually means mandatory swimming cap (men & women, long & short hair, doesn't matter), "Speedo"-style swimsuits for men (no shorts), and no visible tattoos.
In my answer below, I use the Nagai Park swimming pool as a reference, but I think it is almost identical to other swimming pools in Japan.
It is totally not allowed to swim in any direction parallel to the width of the pool.
Almost the same as what was already mentioned by @jpatokal in his answer, each lane has its own purpose (probably scheduled differently everyday and posted at the lane). For example,
the first lane is only for ones who want to walk in the water (physical therapy).
the second lane is for ones who want to either walk or swim (beginner swimmers).
the third lane is for one who want to swim slowly (beginner).
the forth lane is for one who want to swim fast (professional).
the other lanes are for school students.
Each lane is marked with a colored rope. Unfortunately, each lane is also divided into 2 sub-lanes but without any colored rope. We swim on the right part and return on the left part. This division makes me sometimes accidentally kick other people coming from the opposite direction. So keep your eyes open.
On the same part, it is not allowed to chase and overtake the person swimming in front of you because you will occupy the left part and hit the oncoming swimmer.
Watches and necklaces (among others) are not allowed to be worn in the water.
I have purchased one month unlimited ticket for 4900 yen. I can make use of the pool everyday (except for some national holidays) at any time during the work day.
The water is disinfected by using chlorine rather than ultra violet.
