Bounding the efficiency gain of differentiable road pricing for EVs and GVs to manage congestion and emissions

Increasing concerns about air pollution and the promise of enhancing energy security have stimulated the growth of electric vehicles (EVs) worldwide. Compared with gasoline vehicles (GVs), EVs have no emissions and are more environmentally friendly to the sustainable transportation system. Since these two types of vehicles with different emission externalities and observable differences, in this paper, we propose a differentiable road pricing for EVs and GVs to simultaneously manage congestion and emissions by establishing a two-class bi-objective optimization (TCBO) model. First, we investigate whether the differentiable road pricing can induce user equilibrium pattern into a unique pareto-efficient pattern. Then performance of the bi-criteria system optimal is measured by bounding the deviation gap of the Pareto frontier. Specifically, we bound how far the total system travel time and total system emissions at a given Pareto optimum can deviate from their respective single-criterion based system optimum. Finally, we investigate the maximum efficiency gain of the bi-criteria system achieved through implementing differentiable road pricing by comparing total system travel time and total system emissions under two states. After defining two types of price of anarchy (POA), the theoretical bound for the worst possible ratio of total system travel time\ total system emissions in user equilibrium state to the total system travel time\ total system emissions in Pareto-efficient state is derived out. In order to validate the feasibility of theoretical bound, we conduct case studies to calculate the numerical bound of POA based on two Chinese cities: Shenzhen and Lasa. Overall, quantifying the maximum efficiency of differentiable road pricing is beneficial for improving the network designing, policy implementation and social efficiency with regard to congestion and emissions caused by EV and GV users.