In other words, the velocity of a car multiplied by the time increment can never exceed the distance to the car in front of it. Third, there will be a maximum velocity, i.e., a speed limit. Fourth, every car always travels as fast as it can, keeping to the preceding rules. Although it is unrealistic, we will assume for now that every car is a point, i.e., has length 0, and two cars may occupy the same point at the same time, though one of them must always be thought of as being infinitesimally behind the other. In this situation, the following car would have to set its velocity to zero, in keeping with the rules about velocity and following distance.
Minimum velocity is zero, which, of course, can occur in a severe traffic jam.
One of the branches of the Y will have to be given right of way, so that, if two cars reach the merge point at the same time, we will know which one should be placed behind the other. To begin, there will be no upper upper or lower bound on acceleration, only on velocity. We will probably begin by simply sending cars into the top of the Y at a constant rate each with the maximum velocity and minimum following distance, possibly staggered. Such a model should not take too much time to develop, and then the goal will be add in realism. For example, one should assume a maximum acceleration which possibly varies with velocity.