Order parameter model for unstable multilane traffic flow

TL;DR

This paper introduces an order parameter model to describe phase transitions and hysteresis in unstable multilane traffic flow, linking vehicle correlations to driver behavior and analyzing cluster formation.

Contribution

It proposes a novel order parameter approach to model lane correlations and phase transitions in traffic flow, supported by experimental data and simplified cluster analysis.

Findings

Explains the sequence of traffic phase transitions and hysteresis.

Identifies correlations due to 'fast' drivers as key factors.

Characterizes vehicle flow independence in traffic jams.

Abstract

We discuss a phenomenological approach to the description of unstable vehicle motion on multilane highways that explains in a simple way the observed sequence of the phase transitions "free flow -> synchronized motion -> jam" as well as the hysteresis in the transition "free flow <-> synchronized motion". We introduce a new variable called order parameter that accounts for possible correlations in the vehicle motion at different lanes. So, it is principally due to the "many-body" effects in the car interaction, which enables us to regard it as an additional independent state variable of traffic flow. Basing on the latest experimental data (cond-mat/9905216) we assume that these correlations are due to a small group of "fast" drivers. Taking into account the general properties of the driver behavior we write the governing equation for the order parameter. In this context we analyze the instability of homogeneous traffic flow manifesting itself in both of the mentioned above phase transitions where, in addition, the transition "synchronized motion -> jam" also exhibits a similar hysteresis. Besides, the jam is characterized by the vehicle flows at different lanes being independent of one another. We specify a certain simplified model in order to study the general features of the car cluster self-formation under the phase transition "free flow <-> synchronized motion". In particular, we show that the main local parameters of the developed cluster are determined by the state characteristics of vehicle motion only.