A CA Hybrid of the Slow-to-Start and the Optimal Velocity Models and its Flow-Density Relation

TL;DR

This paper introduces a cellular automaton hybrid model combining the optimal velocity and slow-to-start models, analyzing its flow-density relations and traffic phases through mathematical derivations and limits.

Contribution

It presents a novel CA hybrid model of traffic flow, deriving flow-density relations and analyzing traffic phases using ultradiscretization and continuous limits.

Findings

Multiple traffic phases including free flow and slow flows identified.

Flow-density relations derived from stationary flow properties.

Model captures metastable states in traffic dynamics.

Abstract

The s2s-OVCA is a cellular automaton (CA) hybrid of the optimal velocity (OV) model and the slow-to-start (s2s) model, which is introduced in the framework of the ultradiscretization method. Inverse ultradiscretization as well as the time continuous limit, which lead the s2s-OVCA to an integral-differential equation, are presented. Several traffic phases such as a free flow as well as slow flows corresponding to multiple metastable states are observed in the flow-density relations of the s2s-OVCA. Based on the properties of the stationary flow of the s2s-OVCA, the formulas for the flow-density relations are derived.