Pricing Environmental Externality in Traffic Networks Mixed With Fuel Vehicles and Electric Vehicles

Serious roadside pollution in congested urban areas is an ongoing problem in many densely populated cities. While the current control measures on traffic pollution have reduced particulate matter, new solutions by emerging vehicular technologies can help protect citizens from exhaust-gas emissions. The electric vehicle (EV) is a promising solution to alleviate traffic-induced pollution in urban areas. However, traffic flow will be mixed with fuel vehicles (FVs) and EVs before the FV would be phased out. In this paper, traffic management by road pricing is introduced to reduce the tailpipe emission of the protected area by imposing environmental capacity constraints for network traffic mixed with EVs and FVs. Second-best toll pricing schemes are formulated as side constrained user equilibrium problems for both fixed demand and elastic demand cases. Both the tailpipe emission of FVs and the energy consumption of EVs are assumed to depend nonlinearly on network traffic conditions. Although the EVs do not contribute to the tailpipe emission, all vehicles contribute to congestion externality that induces more emission of FVs. Therefore, both types of vehicles are charged, but the toll on FVs is significantly higher than that on EVs. A new projected dynamics based algorithm is introduced to solve the toll from the Lagrange multiplier associated with the environmental constraint apart from the equilibrium flow. Numerical examples are conducted to evaluate the equilibrium cost and toll, and to analyze the impacts of EV penetration rate on the pricing scheme.