Abstract
The research presents a study of developing and verifying mathematical models for traffic control at traffic light intersections. The research's primary goal is to create accurate and reliable models that optimize the operation of traffic lights and the distribution of traffic flows, which contributes to reducing the waiting time at intersections and reducing harmful emissions into the atmosphere from idling cars. The study examines various criteria for evaluating the effectiveness of traffic management, such as total travel time, number of stops, traffic intensity, and average delays. The developed models consider the dynamics of urban traffic flows, including the characteristics of vehicles and the random nature of the flow. The results demonstrate that using mathematical models allows you to significantly improve the ecological situation in cities, increase the capacity of roads, and increase the overall speed of vehicles. The study emphasizes the importance of developing accurate mathematical models for increasing traffic management efficiency and improving city environmental safety.