A hybrid of the optimal velocity and the slow-to-start models and its ultradiscretization

TL;DR

This paper introduces a new ultradiscretizable traffic flow model combining the optimal velocity and slow-to-start models, revealing phase transitions and metastable states through cellular automata simulations.

Contribution

It extends ultradiscretization techniques to create a hybrid traffic model, generalizing previous ultradiscrete optimal velocity models.

Findings

Observation of phase transition from free to jam states

Existence of multiple metastable states in traffic flow

Numerical validation via cellular automata simulations

Abstract

Through an extension of the ultradiscretization for the optimal velocity (OV) model, we introduce an ultradiscretizable traffic flow model, which is a hybrid of the OV and the slow-to-start (s2s) models. Its ultradiscrete limit gives a generalization of a special case of the ultradiscrete OV (uOV) model recently proposed by Takahashi and Matsukidaira. A phase transition from free to jam phases as well as the existence of multiple metastable states are observed in numerically obtained fundamental diagrams for cellular automata (CA), which are special cases of the ultradiscrete limit of the hybrid model.