Study of the Mathematical Model of the Stability of the Traffic Flow in the Sections of the Road Network of the City

The paper presents the results of the research of the mathematical model of the stability of the traffic flow on the sections of the city's street and road network when external factors change. Based on the modeling results, it is proposed to divide all factors affecting the stability of the traffic flow into three groups. The first group of factors characterizes the construction of the vehicle: the length of the vehicle, the weight of the vehicle, the power of the engine. The second group of factors is called time factors, which take into account: the driver's reaction time to a change in the road situation; time for a maneuver that can be used by the car in case of a change in the road situation; the total time of delays while driving along the route. The third group of factors takes into account the peculiarities of the construction of the infrastructure of the road environment. Such factors include: the number of traffic lanes on the roadway; the number of pedestrian crossings and traffic lights. Based on the results of modeling, a rating of factors affecting the amount of traffic flow stability margin is presented. The simulation results proved that, in the first place, the impact on the loss of stability of the traffic flow is the time for the maneuver that the car can use in the event of a change in the road situation and the number of pedestrian crossings and traffic lights on the controlled section of the road. When the listed factors change, the robustness criterion has minimal values. In second place in terms of influence on is a group of factors that take into account the driver's reaction time to a change in the road situation and the number of traffic lanes on the roadway. In third place is a group of factors that take into account the length of the car and the weight of the car. It is proved that the mathematical model of traffic flow stability has limitations regarding its application. The limitations are related to the definition of the initial data for the simulation. It is necessary to determine the flow density on the controlled section of the road network. In addition, statistically determined values are the reaction time of drivers to a change in the road situation and the presence of pedestrian crossings and traffic lights on the controlled section of the road.