Analytical Results for a Small Multiple-layer Parking System

TL;DR

This paper analyzes a small multilayer parking system, showing that the particle density in higher layers approaches 1/2, indicating increased capacity driven by randomness, with conjectures extending to larger systems.

Contribution

It provides an analytical proof of density limits in a 3-layer parking system and conjectures applicability to larger systems.

Findings

Density in the center approaches 1/2 in higher layers

Capacity increases significantly compared to the first layer

Results are driven by a purely random process

Abstract

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.