The Effect Of Delay Times On The Optimal Velocity Traffic Flow Behavior

TL;DR

This study numerically examines how delay times in a mixed fast-slow vehicle traffic model influence flow behavior, revealing phase transitions, metastability, and complex traffic patterns depending on delay parameters.

Contribution

It introduces a detailed analysis of delay effects on the optimal velocity traffic model, highlighting new phase transition phenomena and complex traffic structures.

Findings

Large delay times cause qualitative changes in traffic flow patterns.

First order phase transitions occur at certain densities.

Metastability and hysteresis emerge above a critical delay threshold.

Abstract

We have numerically investigated the effect of the delay times $\tau_f$ and $\tau_s$ of a mixture of fast and slow vehicles on the fundamental diagram of the optimal velocity model. The optimal velocity function of the fast cars depends not only on the headway of each car but also on the headway of the immediately preceding one. It is found that the small delay times have almost no effects, while, for sufficiently large delay time $\tau_s$ the current profile displays qualitatively five different forms depending on $\tau_f$, $\tau_s$ and the fractions $d_f$ and $d_s$ of the fast and slow cars respectively. The velocity (current) exhibits first order transitions at low and/or high densities, from freely moving phase to the congested state, and from congested state to the jamming one respectively accompanied by the existence of a local minimal current. Furthermore, there exist a critical value of $\tau_f$ above which the metastability and hysteresis appear. The spatial-temporal traffic patterns present more complex structure