I've done a bit of time as a petroleum mechanic.

There are 2 ways a gas pump can work: Either you have a pump at the fuel tank that is activated by the switch on the gas pump that then runs through the dispenser and through the hose (and whatever anti-siphon measures you need along the way), or you have a line that runs to the gas pump at the dispenser, which then goes into your car.

Generally, if the pump slows down, there aren't a lot of moving parts so it's going to be one of a very small number of things. It's possible there's a piece of debris in the tank that blocked the inlet to the pump. It's possible that the different pumps connect to a shared inlet so they are fighting over the fuel coming into the system and multiple people are running the pumps at once. Another thing that it could be is the filters are getting plugged. Often they use fuel filters to ensure grit doesn't end up in your fuel tank, and they can get clogged up.

In general, it either indicates a maintenance issue or a design issue. If I were taking a look, I'd start on the maintenance end.

If it's busy and slow, it's likely because pumps share lines and the pumps aren't sized for the number of spots. It's also obvious when the pump speeds up after someone stops.

If it's not busy and it's slow, then it's a maintenance thing and the pump is in need of service.

It's probably just one pump/motor per physical stand and if both sides of the stand are used at the same time you get half the flow rate since you're sharing it with your neighbor.

I worked at a gas station about 20 years ago, so things may have changed since then. When our pumps started running slow, it was almost always due to the pump filters nearing their end of life. They would get clogged with the minerals and sediments in the tank.

I’ve noticed when someone else stops pumping at the station it speeds up. I think they are all connected and the main line has a maximum output. At least at my Sam’s Club they are definitely that way.