The article defines the regularities in the influence on the traffic flows dynamics in cities using mathematical modelling, taking into account the historical features of this process, as well as the most relevant issues. In the queuing theory obstruction of free movement is considered a service, and the duration caused by this delay is called service duration, which is not applicable to the delay of transport at intersections. By means of mathematical modelling, the dependence of the influence of increasing the congestion degree on the increasein vehicle delays was determined. Results of studying transport flow characteristics in large cities should be considered when determining loading of urban passenger vehicles and calculating duration of delivering passengers to their destination. Application of the proposed mathematical model will help to reduce the probability of traffic congestion in the urban transport network of large cities, providing high-quality public transport services to clients.

Purpose. Creation and substantiation of the measures for adopting the supporting structure of the multipurpose semi-car to carry cargoes that need weather protection. Methodology. For the adaptation of supporting constructions of semi-cars to carriage of cargoes that need weather protection, it was proposed to apply a removable roof manufactured from composites. As the application of a removable roof enlarges the volume of the container of the semi-car, the authors defined the load on its construction with the help of mathematical modeling. The authors see semi-car as a system which includes three components – a supporting construction having a roof with two carts. The Runge-Kutta method was used to calculate the main dynamic parameters of the semi-car. These defined dynamic parameters were accounted during calculation of the strength of the dismountable roof. Graphic spatial modeling of a semi-car with a dismountable roof was performed in the SolidWorks software kit. The calculation of solidity is implemented by the method of ultimate elements using the SolidWorks Simulation program kit. The original frequencies and forms of vibrations of the supporting construction of the semi-car are performed in this research. Findings. The outcomes of a mathematical model of the dynamic loading of the supporting construction of the semi-car having a dismountable roof set that the obtained dynamic parameters are not higher than the allowable values. The acceleration of the semi-car supporting construction in the gravity center made approximately 4.5 m/s2. The vertical dynamic ratio amounts to 0.53. The car motion is evaluated as “excellent”. It was found that when the vertical load acts on the dismountable roof, the maximum tension emerging inside is 173.2 MPa. When concentrated load affects the dismountable roof, the biggest tensions are focused on the zones of its attachment to the upper strapping of the casing, and makes 205.7 MPa. It can be seen from the modal analysis that the first original frequency of the semi-car casing is equal to 9.6 Hz, which is more than the allowable value – 8 Hz. Originality. Models for determining the loading of the supporting construction of the semi-car having a dismountable roof from composites within the general modes of loading operation are given in this study. Practical value. The study results allow expanding the applicability of semi-cars by adapting them to the carriage of cargoes, which need protection from weather effects and can increase the performance of railroad carriage.