Optimization models of rush hour transit system based on Cournot behavioral assumption

Based on Cournot behavioral assumption, with the consideration of passenger travel behavior during rush hour, we investigate transit system optimization. The interval of transit vehicle is assumed to be determined by transit companies, while the total number of vehicle is the result of passengers' equilibrium riding behavior. Considering demand elasticity, arrival early penalty and congestion in carriages, we propose two optimization models of the rush hour transit system on the base of passengers' equilibrium riding behavior. The first model aims at maximizing the net benefit of the system, gives the optimal value of the demand realized totally and the number of trains required. The second model maximizes every company's profit in an oligopoly market regime, determines the optimal time interval of dispatching trains. Numerical results are presented for illustrating analytical results. It is found that, the number of transit company could influence system manifestation, which could be cutthroat competition without government regulation, accompanied by the phenomenon of wasting social resources.