A method has been developed to simulate propagation of train delays in branched railroad ranges using modified epidemiological SIR models. These models take into account the mutual influence of trains with different priorities in the flow. This makes it possible to study the heterogeneous dynamics in the propagation of delays among trains of different priorities. To consider the propagation of the primary delay in space and time, it is proposed to represent the topology of the railway network in the form of an undirected graph with reference to the edge of the graph in the mathematical system of differential equations of the SIR model. This unifies the process of constructing SIR models for each edge (section) of the network graph and reduces the dimension of the problem. To take into account the influence of the "network effect", it is proposed to determine the transit coefficient for each station of the section. This coefficient helps calculate the number of delayed trains for adjacent sections. To set SIR models, it is proposed to use empirical data on the propagation of the average delay in the standard traffic schedule in the corresponding section. For the sequential solution of SIR models corresponding to interconnected network sections, an algorithm is applied to turn the network graph into a directed tree the root of which is the station where the delay occurs. Tests on modelling the propagation of train delays in the railway network are carried out taking into account the mutual influence of different categories of trains in the flow and the built-in time reserves for the restoration of movement. The obtained simulation results have confirmed the adequacy of the solutions and helped quantify the influence of primary delays and the amount of time reserve in the schedules of trains of various categories on the reliability of the standard train schedule
6 chain to the destination becomes more complicated. This leads to an increase in the operating costs of a railroad system compared to railroads that follow the system of train traffic on schedule. To improve the competitiveness of a railroad system within which the traffic of trains fails to follow a timetable, it is important to build the functional for a periodic notification about the state of train dispatch. One of the important notification functions is the calculation of the estimated time of arrival (ETA) of a cargo dispatch [2]. Within the framework of the ETA calculation, which is determined for a cargo dispatch at each railroad station 1. Introduction Given the conditions of automation and digitalization of all industries, increasing the level of predictability of the technological process of a rail system transportation is a necessary requirement to reduce the cost of supply chains [1]. The operating model of railroad systems without following the schedule of freight trains possesses a considerable degree of uncertainty in the cargo transportation process. In such systems, the possibility of predicting the duration of operations involving cargo dispatch along a transportation
It is important to find rational values of time reserves to compensate for delays during train movement to ensure train schedule reliability. This study proposes to investigate the impact of different categories of trains and their time reserve on schedule reliability. The main purpose of the study is to develop a method for studying the extent of the impact of time reserve on train schedule reliability based on the epidemiological model. Mathematical train delay propagation at the section model has been developed on the basis of the Susceptible – Infected – Removed (SIR) epidemiological model of adaptation type (taking into account the effect of using different train categories. It is suggested to use a binary genetic algorithm to search for parameters of delay propagation rate in the SIR model. According to a specially developed data acquisition algorithm, empirical data on the propagation of train delays at the station were obtained. Experimental studies have been carried out to search for train delay propagation velocity coefficients in the SIR model. The train movement restoration results during a delay at the station are given to study the impact of the time reserve value on train schedule reliability, taking into account the speed recovery delay set in the SIR model. The simulation results confirm the developed mathematical model adequacy.
In the context of the search for strategies for the development of railway infrastructure, it is important to theoretically substantiate the choice of constructive and organizational measures that will allow the development of promising passenger and freight traffic. This study proposes an approach to determining the rational parameters of energy efficient technology for the transportation of freights on the site in the context of the implementation of one of the reconstruction measures - modern dispatch centralization of train traffic control. The main aim of research is to develop a methodology for determining an energy efficient technology for transporting freights on a single-track railway line. It is proposed to use analytical methods for calculating the average speed of trains with a combination of micromodeling of traction characteristics of freight trains of different mass. Theoretical calculations of the change in the section speed were carried out when the dispatch centralization was introduced, taking into account the choice of various options for the mass of freight trains. The calculations performed for a single-track line and the dependences of the cost change per one shipped carriage and the section speed on the train mass were obtained, which made it possible to determine the optimal parameters of the energy-efficient technology for the transportation of freights by the line. The proposed method for determining the energy efficient technology for the transportation of freights can be used in the technical and economic calculations of projects for the implementation of various systems of train dispatch control on single-track railway lines.
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