Traffic flow models with 'slow-to-start' rules

TL;DR

This paper studies traffic flow models with 'slow-to-start' rules, revealing how these modifications affect flow-density relationships, symmetry properties, and phase transitions, with findings supported by analytical and simulation methods.

Contribution

It introduces modified traffic models with 'slow-to-start' rules, analyzes their fundamental diagrams, and uncovers a new phase transition to a jammed state.

Findings

Modified rules break particle-hole symmetry.

Exact solutions for basic model with v_max=1.

Discovery of a new phase transition to jammed state.

Abstract

We investigate two models for traffic flow with modified acceleration ('slow-to-start') rules. Even in the simplest case $v_{max}=1$ these rules break the 'particle-hole` symmetry of the model. We determine the fundamental diagram (flow-density relationship) using the so-called car-oriented mean-field approach (COMF) which yields the exact solution of the basic model with $v_{max}=1$. Here we find that this is no longer true for the models with modified acceleration rules, but the results are still in good agreement with simulations. We also compare the effects of the two different slow-to-start rules and discuss their relevance for real traffic. In addition, in one of these models we find a new phase transition to a completely jammed state.