It can be modelled, but with a slight twist. If in a water analogy we prefill the maze with a water and then connect it to a source and a drain, then water leve

It can be modelled, but with a slight twist. If in a water analogy we prefill the maze with a water and then connect it to a source and a drain, then water level will raise near the source and fall near the drain. We'll see then how it propagates through the maze, these waves will meet somewhere, then some more hard to describe action will follow and then the system will settle to a dynamic equilibrium. This way the water level changes probably can propagate faster then water moves. Though probably to get this result we'll need to make a "deeper" maze. I mean make walls higher so a cross section of a path would have bigger area, so a slow flow multiplied by this area would give us a big volume of a water moving. Big enough to raise level of a water fast in a whole section of the maze.