A complete system of conditions for uncongested traffic of vehicles in front of a traffic light at a symmetrical two-lane intersection

The problem of optimizing the transport system of cities has not yet been solved. One of the urgent practical problems is the problem of the operation mode of traffic light at the city intersections. The present article is based on the theoretically proven by M. Lighthill and J. Whitham and now widely known condition of non-accumulation of vehicles in front of an intersection traffic light operating in two modes (red light on, green light on) along each of the intersection routes. Although more than 70 years have passed since the Lighthill-Whitham condition was proved, this condition is not used in practice, and is treated as a purely theoretical result. However, the Lighthill-Whitham condition may quite simply get a practical interpretation and average values of the traffic flow would be obtained, based on measurements of the intersection lanes' traffic. Based on the Lighthill-Whitham condition, the paper proves the general condition (necessary and sufficient) to avoid the congestion of vehicles in front of a traffic light at an intersection as a whole and a sufficient condition for blocking an intersection, which makes it possible to identify symmetrical two-lane intersections along each of the highways in the city, that are close to blocking. An optimal solution to the problem of a traffic light is presented based on a commutation relation that sets the limiting times for the green traffic light to be on along each of the intersection routes. It was a symmetrical two-lane intersection that was considered in the work, for the reason that such intersections make up a larger part of urban intersections.