Optimization of quantity of passenger transport facilities in urban transport subject to waiting loss

The paper focuses on formalizing the task of choosing the optimal number of public transport for minimizing total losses of the transport system and all passengers (where passenger loss is expressed by their waiting time at the stations). As for the research tool, the queuing theory apparatus was chosen. There was introduced a nonlinear function that estimates passenger loss, given the relations for finding two parameters describing the function. A system of equations describing possible states of the queuing system under consideration in the stationary mode of its operation has been obtained. Similar equations are derived for the case when the rate of passengers arriving to the stations depends on the number of passengers already waiting at the stations, which is typical for cases where there are a small number of possible sources of passenger arrival to the station, e.g. in industrial districts of the cities.The optimization problem of finding the optimal number of vehicles is formulated by minimizing the total losses of the transport system and all passengers. The solution of the problem obtained is reduced to solving the system of equations using Newton method as one of the most effective methods for solving systems of equations defined by analytic expressions. Software implementation of the procedures given in the work will reduce the number of vehicles for passenger transportation to a certain acceptable level, thereby reducing the amount of traffic on urban roads.