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The operational stock of signals and interlockings is necessary to ensure the uninterrupted operation of the electric interlocking systems in the event of their component failure. The existing standards for the composition and number of signals and interlockings available in the operational stock of railway stations are not mathematically based. It is considered the task of justifying the number of signals and interlockings in the operational stock of railway stations, and the factors affecting its quantity are indicated. It is proposed the mathematical model for rationing the amount of equipment necessary to ensure the uninterrupted operation of station signals and interlocking systems with a specified probability. The process of using and replenishment of reserve equipment is described using the the single-channel Markov queuing system model with a limited queue. The proposed probabilistic methodology approbation for the rationing of the amount of reserve equipment was carried out at the stations of the two Belarusian Railway divisions totaling to 58 stations equipped with relay and computer-based electric interlocking. It is shown the efficiency of the calculated amount of equipment in comparison with the existing values.

The problems of railroad design technical reconstruction aimed at ensuring train protection in introduction of high-speed traffic on the rail lines have been addressed. The description of railroad technical system with certain specific features has been proposed. The pair of mutually dual problems regarding the optimal reconstruction of railway curves for raising train speeds at minimal capital investments has been addressed. The problem of determining the optimal speeds of trains of each category under optimum outer rail cant, increase of the unbalanced acceleration value, compliance with the condition of uniform load on rail tracks, comfortable carriage of passengers, in which reduced costs on increased speeds in curved tracks will be minimal has been formulated. To achieve the goals of the study, mathematical optimization techniques and algorithms of analysis of the rail lines of different nature are used. This, by finding and value engineering optimization, allows to minimize high-value and lengthy procedures of physical simulation. As a problem-solving technique, Lagrange multiplier method and its applicability have been proposed. Numeral solution to the problem of selection of certain stretches for increasing rolling stock speeds on operating lines without reconstruction or with minimum expenses on reconstruction of contour of track has been reviewed.