Delay of vehicle motion in traffic dynamics

We demonstrate that in the Optimal Velocity Model (OVM) delay times of vehicles coming from the dynamical equation of motion of OVM explain the order of delay times observed in actual traffic flows without introducing explicit delay times. This implies that the explicit delay time is not important in contrast to the traditional car following models, in which the explicit delay time was thought to be essential to explain realistic traffic flow. Effective delay times in various cases are estimated: the case of a leader vehicle and its follower, a queue of vehicles controlled by traffic lights and the many-vehicle case of highway traffic flow. The remarkable result is that in most of the situation for which we can make a reasonable definition of an effective delay time, the obtained delay time is of order one second. This agrees with the observed data very well.