Optimal Parameters of Service in a Public Transportation Market with Pricing

The problem of choosing the optimal parameters of service by carriers in public transport passenger flows is considered. This problem is modeled as a two-stage game. At the first stage, the players (carriers) select the parameters of their service (the number and schedule of vehicles, etc.). At the second stage, the players announce the prices of service and the consumers choose an appropriate service. The Wardrop equilibrium is applied to the competition model with rational consumers preferring the carriers with minimum cost, where the cost of service includes the price and also the expected trip time. The equilibrium in the pricing game is found and the optimal parameters of service as a solution to a noncooperative game are determined. Some results of computer simulations are presented.