Inter-particle gap distribution and spectral rigidity of totally asymmetric simple exclusion process with open boundaries

TL;DR

This paper derives exact and approximate formulas for inter-particle gaps and spectral rigidity in the TASEP model with open boundaries, linking statistical physics to traffic flow analysis.

Contribution

It provides the first analytical expressions for gap distribution and spectral rigidity in open-boundary TASEP, with validation against numerical simulations.

Findings

Exact gap distribution formulas derived and validated.

Approximate formulas for large system sizes established.

Spectral rigidity estimated and discussed in traffic context.

Abstract

We consider the one-dimensional totally asymmetric simple exclusion model (TASEP model) with open boundary conditions and present the analytical computations leading to the exact formula for distance clearance distribution, i.e. probability density for a clear distance between subsequent particles of the model. The general relation is rapidly simplified for middle part of the one-dimensional lattice using the large $N$ approximation. Both the analytical formulas and their approximations are successfully compared with the numerical representation of the TASEP model. Furthermore, we introduce the pertinent estimation for so-called spectral rigidity of the model. The results obtained are sequentially discussed within the scope of vehicular traffic theory.