Multiple-Layer Parking with Screening

TL;DR

This paper investigates a multilayer parking system with screening, analyzing how particle density evolves across layers and deriving its asymptotic limits.

Contribution

It provides a mathematical analysis of particle density growth in a multilayer parking model with screening, establishing explicit asymptotic density values.

Findings

Asymptotic density increases from 1/3 on the first layer to (10 - √5)/19 on higher layers.

The study characterizes the density distribution in a multilayer parking system with screening.

Mathematical proof of density limits in the multilayer model.

Abstract

In this article a multilayer parking system with screening of size n=3 is studied with a focus on the time-dependent particle density. We prove that the asymptotic limit of the particle density increases from an average density of 1/3 on the first layer to the value of (10 - \sqrt 5 )/19 in higher layers.