Congestible goods describe situations in which a group of people share or use a public good that becomes congested or overexploited when demand is low. We study experimentally a congestible goods problem of relevance for parking design, namely how people choose between a convenient parking lot with few spots and a less convenient one with unlimited space. We find that the Nash equilibrium predicts reasonably well the competition for the convenient parking when it has few spots, but not when it has more availability. We then show that the Rosenthal equilibrium, a bounded-rational approach, is a better description of the experimental results accounting for the randomness in the decision process. We introduce a dynamical model that shows how Rosenthal equilibria can be approached in a few rounds of the game. Our results give insights on how to deal with parking problems such as the design of parking lots in central locations in cities and open the way to better understand similar congestible goods problems in other contexts.