Mathematical Modeling of Transportation Flows

This paper discusses mathematical modeling of transportation routing, the process of creating mathematical models that describe and predict the behavior of traffic flows, such as public transportation movements, based on various factors such as road networks, road conditions, and vehicle flows. To implement the software and mathematical support that allows to analyze the work of public transport system with changing input parameters, modeling factors, and target indicators, the method of simulation models was used, as well as the method of simulation experiments, including optimization experiments. The General Purpose Simulation System package was used to optimize the route of public transport. Experimental investigations of the developed mathematical model on optimization of public transport route using simulation model have been carried out. A mathematical and simulation model of Kazan bus route No. 54 is developed. The article presents the results of creating a simulation application for conducting computational experiments and optimizing the operation of public transport, the abovementioned route.