The purpose of the article was to find the inner properties and regularities of anti-aircraft missile grouping’s air defense battle, and based on these regularities to develop and evaluate the adequacy of models as tools for forecasting the results of a battle. To achieve the goal, an example of a real battle and a special model development method were used. The method made it possible to identify the main properties and the inner law of battle, to select a statistically valid mathematical modeling tool in the class of Markov processes with continuous time and discrete states, to develop the desired models with an analytical representation of the inner law of battle, to check their adequacy and to evaluate the accuracy of forecasting by models using the example of a real air defense battle.

The structural components of the rail track, including rails, deteriorate in operation. However, some of them retain their operational characteristics and can be reused. This practice has found wide application on Ukrainian railways and shown a lot of self-evident advantages, among which the basic one is a rational use of material and technical means. Besides, development of a used rail system for underground railways may also optimize the track facility system for such specific conditions. The article presents results of the research into the change of the crumbling depth on the roll surface (the main rail defects of underground railways); it allowed the authors to conclude about the possibility to reuse rails for underground systems. Moreover, assessment of interacting forces in the wheel/rail system and the crumbling volume made it possible to determine rational application for used rails. The proposed system takes into account all the features of operating the railway track in underground systems, and also allows more efficient use of the residual rail resource without reducing the necessary level of traffic safety.