  in this article a multilayer parking system of size n=3 is studied. We prove
that the asymptotic limit of the particle density in the center approaches a
maximum of 1/2 in higher layers. This means a significant increase of capacity
compared to the first layer where this value is 1/3. This is remarkable because
the process is solely driven by randomness. We conjecture that the results
applies to all finite parking systems with n larger or equal than 2.
