On the influence of delays in route trains on the recovery of train graphics

Abstract

The main goal of railway transport is the timely delivery of passengers and goods, which  cannot always be achieved. In the course of its work railway transport is faced with emergency situations: technical, technological, natural and man-made. In the event of such failures, the main thing is considered to be the minimization of time losses, and the reduction of the duration of system recovery. The size of time losses depends on the nature of the failure, the place of its occurrence, the organization of work to eliminate the consequences. Thus, the failure of the rolling stock at the station results in smaller losses than the failure arising on the stretch with the same rolling stock. The abnormal situation that appeared on the stretch of the double-track section, in general, will require fewer adjustments in the planned order of train passage than on the single-track section. Also, the duration of the restoration of the traffic management system depends on the category of the train delayed due to the failure. The article presents an original approach to describing the process of running circular block trains in the event of a failure, in which the train leaves the starting station with a delay. An algorithm for restoring the system of route reversal on a single-track section is presented, which describes the correction of the system and the result of the failure. The graph of the movement of trains in the coordinate system is depicted, which made it possible to estimate the deviations from the schedule of movement geometrically. Based on such an assessment, a mathematical model of a stable state of the system of running circular block trains is proposed. The proposed description of the stability of the circular routes running, in the form of a model, will make it possible to estimate the train schedule depending on the magnitude of the delays of the described category of trains and the number of constant linear dependencies.