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The development of railway transport is currently impossible to imagine without the use of mathematical models and algorithms. Consider the increase in speeds, reduction of travel time, while minimizing costs, is possible only with the qualitative and full use of the mathematical apparatus. The use of information technologies makes it possible to take an effective decision in the development of a project for the reconstruction of a railway line. The current state of the theory of railway transport is characterized by the presence of a developed system of mathematical models and algorithms for analyzing various features of railways. This opens up possibilities for building an approach to the problems of searching and optimizing design solutions on a mathematical basis, with the reduction to a minimum of costly and time-consuming physical modeling procedures. One of the main tasks that are set for the railway transport in the near future is to increase the speed of trains on existing railway lines with the use of computer technology (computer-aided design). The article deals with the problems of technical reconstruction of the railway plan to increase the speed of train movement. The urgency of the use of computer mathematical methods for the development of an optimal plan for increasing the speed of trains. A pair of mutually dual problems of optimal reconstruction of railway curves to increase the speed of trains with minimal capital investment is considered. As methods for solving the problems posed, the following methods were proposed: the method of steepest descent, a modified method of dynamic programming (the Cattell method), the method of indefinite Lagrange multipliers. The expediency of using each method to solve the problem is indicated. The considered methods allow to implement a number of computer-aided design procedures for the reconstruction of the railway plan.

Increasing speeds on existing railway lines is one of the main challenges facing the Belarusian railway. Through the territory of the republic there are two transport corridors connecting Russia and Western Europe, as well as Ukraine and the Baltic countries. In all of the above countries, the increase in speed on the railways is very fast. Belarus can not stand aside. However, to increase the speed, it is not always enough initial information. To identify the necessary data, methods of decision theory are used. The integral probabilistic criterion method (CPI) allows one to substantiate the road parameters necessary for introducing high-speed traffic on existing lines. The proposed method of decision-making on the choice of technical parameters and equipment of the line, taking into account the uncertainty in the re-design for the high-speed movement of passenger trains. The initial data for determining the CPI is a risk matrix or a matrix of particular criteria. When using the risk matrix for each design decision option i, the dependences of the expectation of losses on the probability of realization of the design conditions p varying in the range from 0 to 1 are compiled. In the article on the proposed methodology, the reduced costs for the variants of design solutions are determined under all possible design conditions. Using these costs, a matrix of private criteria and a risk matrix are formed. A comparison was made of the design decision options for the integral probabilistic criterion, using which the recommendation of choosing the option is unambiguous and is accompanied by a quantitative assessment, which facilitates the task to the decision maker.