The components of the market competition of carriers on passenger transport routes of the city transport
system are considered. It is shown that the demand for transportation can be presented in the form of matrices of passenger correspondence. Due to its fluctuations within some limits, the main issue is its distribution among the routes that form the urban route network. The essence of the level of competition between carriers, which has a growing tendency, has been revealed. It is proposed to use the Likert method and the results of a sociological survey to build a model of the attractiveness of routes as its assessment. The utility function of the route, the optimization function of Lagrange and the model of the choice of the passenger movement path were
constructed. It is taken into account that transport enterprises operate in break-even conditions, and profit is a
limitation when solving the task of improving the quality of public service.