Exact Solutions and Flow--Density Relations for a Cellular Automaton Variant of the Optimal Velocity Model with the Slow-to-Start Effect

TL;DR

This paper presents exact solutions for a cellular automaton model combining optimal velocity and slow-to-start effects, revealing flow-density relations and coexistence of free flow and jams, validated by numerical simulations.

Contribution

It introduces a novel cellular automaton model with exact solutions that capture complex flow behaviors and matches empirical flow-density relations.

Findings

Exact solutions demonstrate coexistence of free flow and jams.

Flow-density relation matches empirical formulas.

Numerical patterns confirm analytical results.

Abstract

A set of exact solutions for a cellular automaton, which is a hybrid of the optimal velocity and the slow-to-start models, is presented. The solutions allow coexistence of free flows and jamming or slow clusters, which is observed in asymptotic behaviors of numerically obtained spatio-temporal patterns. An exact expression of the flow--density relation given by the exact solutions of the model agrees with an empirical formula for numerically obtained flow--density relations.