The problem of respect of the train schedules is important for railways of different countries. It is insufficient to compose the schedule, it is necessary to create and to maintain the optimum conditions for it should be respected. Analysis of fulfillment of schedules and of some mathematical applications used for traffic control and planning shows that there are some less known regular occurrences, useful to plan and assess the density of train flows. For instance there is a widely spread opinion, based on standard equation, that if more trains pass by a given leg then the volume of traffic is bigger. Or less is the interval between the trains, more is traffic capacity use ratio. Practices and researches show meanwhile that the interval between the trains can’t be reduced to arbitrarily small value. Besides, while the inter-train interval reduces, the gap between the actual and idealized traffic capacity grows. The study defines factors to be considered while creating conditions for schedule respect at the branched track divisions. Some tools to control super-density of trains at the track divisions and to optimize the regulations in effect on the freight and passenger traffic are proposed. The whole system of proposed equations and algorithms is aimed at respecting of schedules rather than on scheduling itself.

The tools are proposed to adjust and to make conform to each other the planned volumes of traffic and the traffic capacity of the legs.