Algorithms for an approximate solution of the track possession problem on the railway network segment

Algorithmic and instrumental support for solving problems of railway transport control, based on the presentation of applied problems in the form of optimization statements in which linear programming tools are used, is being developed. Previously proposed models and applied statements are expanded with a new problem of finding a track possession — a time interval at which some sections of the railway network are closed for repair work. To solve it, a mathematical model and an optimization statement are proposed for the simultaneous search for a track possession and a train schedule for a certain segment of the railway network. The original setting is reduced to a mixed integer linear programming problem. To take into account possible computational difficulties in solving the problem, a method for finding an approximate solution is proposed which is based on the formation of a basic schedule of movement and its subsequent correction taking into account the need for the track possession. To find an approximate solution, two algorithms have been implemented. In the first, a basic and adjusted train timetable is built in stages by groups of trains united by the same departure and destination stations, and in the second, stages are carried out one train at a time according to the time of readiness for departure. The results of a numerical experiment are presented.