A problem of finding the best ways to ensure the efficient and safe traffic of aircraft (AC) based on the use of methods of mathematical computer modeling is presented. The choice of one of the alternative options for the AS structure and aerodrome infrastructure is considered. The formulation of the problem and a group of performance indicators for various interested parties in the use of the AS structure and aerodrome infrastructure, based on which the performance criterion is formed, are proposed. Each group is represented by quantitative indicators that can be calculated using computer mathematical modeling. The structure of the AS and the aerodrome infrastructure in the form of vectors consisting of the set of elements, such as the air route (AR) network, ATC sectors, and arrival and departure routes, are determined. A mathematical formulation of the problem of multidimensional conditional optimization is presented, taking into account the proposed restrictions and conditions of use, in which the considered options of the AS structure function. The description of mathematical models and algorithms for calculating the indicators are given. Examples of solving research problems using computer modeling methods based on the complex of simulation modeling of the air traffic management (ATM) system, which is designed to assess the structure of the AS and the infrastructure of the aerodrome, are given.

Major events, for example Olympic Games or FIFA World Cup, are very popular with people from all over the world. The demand for air travel noticeably rises at these periods. In that case, research has to be carried out in order to forecast the traffic flow to make all members of ATM system (airlines, airports, ATC and etc.) ready for it. In this paper the method to figure out the possible structure of air traffic flows will be described. This method also can be used to estimate the optimal aircraft fleet to transport the additional passengers or the optimal usage of available aircrafts. The focus will be on minimizing airline's expenses. The main goal of this study is to transform the task of people transportation into math problem. The way to state optimization problem will be represented. This paper also considers different types of research conditions and suitable constraints for each of them.