Mathematical simulation of the street traffic in the presence of traffic lights

One-dimensional traffic flow in the presence of two-position traffic light is considered. Quasi-linear differential equation of the first order for traffic flow density is used as a model. The problem to be researched is what has to be a relationship between the intervals of a green and red light to prevent traffic jams. The same problem is researched for the two crossing streets in the presence of a traffic light in the intersection. There were obtained conditions when the traffic jam is avoided. An algorithm of numerical solution of similar problems related to the street traffic and specific computations are presented.