Spatio-temporal organization of vehicles in a cellular automata model of traffic with 'slow-to-start' rule

TL;DR

This paper investigates how a 'slow-to-start' rule affects the spatio-temporal organization of traffic in cellular automata models, revealing qualitative differences from the standard NaSch model through analytical and simulation methods.

Contribution

It introduces and analyzes the impact of the BJH slow-to-start rule on traffic patterns, highlighting phase separation and differences from the NaSch model.

Findings

Slow-to-start rule causes phase separation in traffic flow.

Distributions of headways and jam sizes differ significantly from NaSch model.

Qualitative differences in traffic organization are explained by phase separation.

Abstract

The spatio-temporal organizations of vehicular traffic in cellular-automata models with "slow-to-start" rules are qualitatively different from those in the Nagel-Schreckenberg (NaSch) model of highway traffic. Here we study the effects of such a slow-to-start rule, introduced by Benjamin, Johnson and Hui (BJH), on the the distributions of the distance-headways, time-headways, jam sizes and sizes of the gaps between successive jams by a combination of approximate analytical calculations and extensive computer simulations. We compare these results for the BJH model with the corresponding results for the NaSch model and interpret the qualitative differences in the nature of the spatio-temporal organizations of traffic in these two models in terms of a phase separation of the traffic caused by the slow-to-start rule in the BJH model.