The analysis of relationship between speed, flow density and traffic intensity of trains at the railway line was made. The dependences of incoming and outgoing train flows on the train flow density were established. The dependence of incoming flow on the speed and average travel time of trains on the line and the accuracy of speed measurement was also established. Thus, the relationship between speed, density and traffic flow intensity of trains on the railway station was analyzed. There was established that the saturation of traffic capacity causes a drop in average speed. Furthermore, we can conclude that it is impossible to achieve maximum traffic capacity, which is calculated according to analytical formulas. In fact, it was possible to reach approximately90% of traffic capacity compared to analytical calculations. Furthermore, it should be noted that in case there are more than 70% of maximum quantity of trains on a railway line, there is a sharp decrease of the average speed rate.Thus, for each railway line it is necessary to determine the value of rational saturation, and in case it is overloaded it is reasonable to reroute some trains on parallel railway lines.

Выполнен анализ зависимостей между скоростью, плотностью потока и интенсивностью движения поездов на железнодорожном участке. Установлены зависимости выходящего и входящего потоков поездов от плотности поездов на участке, зависимость входящего потока от скорости движения, а также установлена взаимосвязь между средним временем хода поездов по участку и точностью реализации скорости.

The analysis of relationship between speed, flow density and traffic intensity of trains at the railway line was made. The dependences of incoming and outgoing train flows on the train flow density were established. The dependence of incoming flow on the speed and average travel time of trains on the line and the accuracy of speed measurement was also established. Thus, the relationship between speed, density and traffic flow intensity of trains on the railway station was analyzed. There was established that the saturation of traffic capacity causes a drop in average speed. Furthermore, we can conclude that it is impossible to achieve maximum traffic capacity, which is calculated according to analytical formulas. In fact, it was possible to reach approximately 90% of traffic capacity compared to analytical calculations. Furthermore, it should be noted that in case there are more than 70% of maximum quantity of trains on a railway line, there is a sharp decrease of the average speed rate. Thus, for each railway line it is necessary to determine the value of rational saturation, and in case it is overloaded it is reasonable to reroute some trains on parallel railway lines.

In the article the mathematical model of distributing the trainflows is offered that is based on the methods of vector optimization. It is reasonable to use the offered model when there is a necessity to make a decision concerning the train flows running via the railway network under the conditions of the influence of a number of factors.

У статті запропонована математична модель розподілу поїздопотоку, яка заснована на методах векторної оптимізації. Запропоновану модель доцільно використовувати при необхідності прийняття рішення щодо пропуску потоків поїздів на мережі в умовах впливу багатьох факторів.