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

Abstract

We have numerically investigated the effect of the delay times $τ_f$ and $τ_s$ 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 $τ_s$ the current profile displays qualitatively five different forms depending on $τ_f$, $τ_s$ 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 $τ_f$ above which the metastability and hysteresis appear. The spatial-temporal traffic patterns present more complex structure