Modeling an urban highway: a statistical physics point of view for a nonphysical system

TL;DR

This paper applies statistical physics concepts to model and analyze a Mexican highway as a cellular automata system, demonstrating how simple measures like standard deviation can reveal system order and impact traffic efficiency.

Contribution

It introduces a novel approach using thermodynamic variables, especially standard deviation, to analyze discrete traffic systems and assess the effects of highway modifications.

Findings

Standard deviation can effectively measure order in traffic systems.

Modifications to the highway reduced travel time by up to 32%.

Traffic system behavior remained stable without interventions.

Abstract

Nowadays, methodologies coming from studying physical systems are being applied to the description of a wide variety of complex systems. In particular, one can study thermodynamical methods to describe the overall behavior of many systems, independent of the precise microscopic construction. In this paper, a real Mexican highway is studied as a cellular automata system using available official data released by the Mexican Government. The system studied is the Cuernavaca bypass which was modified in 2016. Official data allows to compare the highway before and after the modifications. As more complex thermodynamic variables such as entropy is difficult to define and measure in discrete traffic models, it is shown how other more simple variables such as the standard deviation can be enough to have a complete analysis of the system. More specifically, it is shown how standard deviation can be seen as a measure of order. Results from the study of the highway show how, taking a minimal measure such as ordering the transit of heavy trucks can reduce up to 32\% the travel time from one end to another. Otherwise, travel times stays practically constant with respect to the original system.