Abstract
One-dimensional traffic flow in the presence of two-position traffic lights is considered. A quasi-linear differential equation of the first order for traffic flow density is used as a model. The problem to be investigated concerns the relationship that has to exist between the intervals of green and red light to prevent traffic jams. The same problem is investigated for a two-road crossing in the presence of traffic lights at the intersection. Conditions leading to the absence of traffic jams on the roads are discovered. Calculations are presented, and an algorithm is provided for the numerical solution for other traffic problems.
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