Digitalization and wide introduction of advanced information technologies, based on the applied application of mathematical methods and models, affect all areas of life of the Russian Federation. The development and implementation of software (software) in the road transport area, when preparing the driver's train, is an urgent task. The article deals with the application of some of the models presented in the works (Georgiev et al. in Stud Syst Dec Control 316:89-97, 2021; Epifanov and Epifanova in Maintenance and repair of cars, 280 p, 2017; Zotov in Investigation and prevention of road accidents, 245 p, 2016) in the simulator systems of driving schools for training and training the drivers. The applied use of algorithms of mathematical models is considered, such as: graph (automatic) model, tensor model and some other models. The implementation of this approach is presented in the form of applied software of the Auto School-Driving training complex. The "Driving School" simulator is designed for motorists and includes: original application software; a hardware and software unit including a computer peripheral device and an analog-to-digital converter; ergonomic workplace of a motorist. The software allows you to teach confident taxiing skills, competent speed switching and braking skills, complex actions in non-standard situations on roads, on highways, in the city, etc., The Driving School-Driving training complex software allows you to prepare in conditions of different grip of car tires with pavement; preparation for driving in winter conditions; modeling and the possibility of combining different weather conditions. All these different modes, the application software allows you to combine when modeling the road situation in virtual space. The original software allows you to typologize cars according to different criteria: by brands; by gearbox type; by drive type; by engine type, etc. In the Applied Software, the possibility of training in of training of motorists to avoid road incidents deserves special attention.

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