Relay Requirement and Traffic Assignment of Electric Vehicles

This article defines, formulates, and solves a new equilibrium traffic assignment problem with side constraintsthe traffic assignment problem with relays. The relay requirement arises from the driving situation that the onboard fuel capacity of vehicles is lower than what is needed for accomplishing their trips and the number and distribution of refueling infrastructures over the network are under the expected level. We proposed this problem as a modeling platform for evaluating congested regional transportation networks that serve plug-in electric vehicles (in addition to internal combustion engine vehicles), where battery-recharging or battery-swapping stations are scarce. Specifically, we presented a novel nonlinear integer programming formulation, analyzed its mathematical properties and paradoxical phenomena, and suggested a generalized Benders decomposition framework for its solutions. In the algorithmic framework, a gradient projection algorithm and a labeling algorithm are adopted for, respectively, solving the primal problem and the relaxed master problemthe shortest path problem with relays. The modeling and solution methods are implemented for solving a set of example network problems. The numerical analysis results obtained from the implementation clearly show how the driving range limit and relay station location reshape equilibrium network flows.