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The main goal of present study is to develop a method for modeling delay propagation in non-cyclic train scheduling on a railroad network with mixed traffic. This will make it possible to explore the dynamics of delay transfer between trains and to identify the most vulnerable points in the timetable of trains. We have devised a method for modeling delay propagation in non-cyclic train scheduling for the rail networks with mixed traffic. It is proposed to apply as a basis of the developed method a mathematical model for the construction of a non-cyclic train timetable. A distinctive feature of the objective function of the mathematical model is taking into consideration the patterns of building a non-cyclic train timetable under conditions of mixed traffic of passenger and heavy-weight or multi-car freight trains, for which it is important to minimize the cost of stopping during motion. The proposed mathematical model was solved based on the multiagent optimization. To account for delay propagation on the railroad network of great dimensionality, we devised a procedure for connecting interdependent sections, which makes it possible to decompose the general problem based on the construction of schedule of trains for separate estimated sections taking into consideration the network effect. We performed an analysis of the dynamics of propagation of secondary delays in non-cyclic train scheduling with detailed patterns of changes in all parameters in time and space. We obtained dependences of the number and duration of delayed trains on the point of occurrence in the timetable of trains along the estimated line of the Ukrainian railroad network. The approach proposed allows the automatization of determining a time reserve in the standard non-cyclic train scheduling based on forecasting the consequences of train delays.

Development of the method for modeling the propagation of delays in non­cyclic train scheduling on the railroads with mixed traffic

Development of the method for modeling the propagation of delays in noncyclic train scheduling on the railroads with mixed traffic