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.

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The article identified the preconditions for the development of the world economy which included the processes of globalization and internationalization. The role of air transport in the world economy is emphasized because its weight grows every year, because it provides the development of tourism, international programs and cooperation between individual regions of the world. There has been an increase in the number of multinational corporations, increasing the mobility of business passengers what is very important for the airlines. The critical analysis of scientific publications made it possible to state that in Ukraine and abroad the development of the air transportation market was studied by many scientists and their contribution to solving a number of scientific problems related to identifying prospects and opportunities for international and national air transportation markets as well as with the optimization of air carriers is important. However, it was found that insufficient research on recent trends and prospects for the development of global and national air transport markets is in the face of new challenges including the outbreak of coronavirus infection COVID-19. It was found that air passenger traffic in the global market has grown steadily in recent years by 7-8% every year and a quarter of sales depend on the regularity of air transportation of which 70% of this type of business determine the vectors of market expansion. The analysis of aviation accidents revealed that they have a very significant impact on the performance of the carrier whose aircraft suffered them. This applies to both reputational and purely financial losses. The problems with the Boeing 737 Max type also became a serious challenge for the aviation industry due to a number of incorrect design decisions of the world’s leading aviation concern and attempts to save on the training of pilots of this type of aircraft. It is noted that modern passengers are trying to minimize the time spent on travel, the trend of fragmentation of the holiday period is growing rapidly. As a result of the analysis of the domestic air transportation market, it was revealed that during 2019 there was an expansion of the market in general, as well as the activities of foreign airlines, travel from Ukraine to Europe and other parts of the world increased rapidly. A radical change in market trends was observed in mid-March 2020, when due to the spread of the COVID-19 coronavirus in the world, quarantine was introduced and regular flights were stopped. The national air carrier Ukraine International Airlines has declared a two-stage period of resumption of work after the end of quarantine. The authors found signs of hybridization of the airline’s business models at the first stage of the restart and the transition to the airline’s business model which has features of both point-to-point models and obvious features of the model of low-cost carriers. Whereas in the second stage the transition to a partial network model with low-cost models is most likely followed by the emergence of a new already stable hybrid business model based on network principles but with stable features of a low-cost airline.

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In the article methodical foundations of transport services logistics management of cargo owners were realized, on the basis of integrated estimation of economic efficiency of holistic progressive logistic chain operation of cargo delivery. In the making of the study, the authors have identified the provision of logistic management conditions by production and mainline rail transport in carrying out transportations. In the successful implementation of finished product loading and arriving cargo processing plans, clear interaction of all logistics chain elements is an important factor, achieved on the basis of introduction of a stable cargo train schedule at sections and the submission of local operation organization in nodes, at sections and stations. On the basis of modelling possible variants of different parameters ratios of the logistic interaction process of production with mainline rail transport, it was determined that at different parameters ratios results can be obtained that will vary by waiting time of carrying out loading in railway cars and waiting time of removal of finished products from manufacturer’s warehouse, required car fleet and loading of material handling vehicles. In this case, the most economical option should be taken as the main condition for ensuring a rational interaction of industrial and mainline rail transport.