Nothing enters at the bottom.
Every deposit starts in the top row and works its way down, one draw at a time, until it reaches the floor and gets served.
Three rows, one exit.
Every withdrawal is served from the bottom row. When it's drawn, the row above drops down to replace it.
Nobody skips ahead. The only way to reach the floor is to have been there longest.
Coming on @base
Sherry cellars in Jerez have used the same trick for centuries.
You only ever draw from the oldest barrels, and the ones above top them up. The cellar never gets emptied.