The effect of delay times on the optimal velocity traffic flow behavior

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 (the current-density relation) 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 a jamming one, respectively. The minimal current appears in intermediate values of tau(s). Furthermore, there exist a critical value of tau(f) above which the metastability and hysteresis appear. The spatial-temporal traffic patterns near the congested-jamming first-order transition is also presented.