Network equilibrium of battery electric vehicles considering drivers' resting behavior

Driving fatigue cost is a major component of vehicle drivers' travel costs in an intercity or regional network. The charging behavior of electric vehicle (EV) drivers, which is generally synchronized with drivers' resting behavior, can contribute to the mitigation of drivers' fatigue, especially after a prolonged driving period. Overlooking the impact of driving fatigue on the travel cost may overestimate the side-effects of the charging behavior for EV drivers, and result in biased flow and charging demand distribution. In this study, by considering the fatigue as part of the travel cost, we make the first attempt to investigate the impact of EV drivers' charging and resting behaviors on their fatigue cost, and thus their travel plans and resultant flow distribution across the network. To this end, a novel network equilibrium modeling framework is first developed to capture the interaction among EV drivers' travel plans, which specify the routing, recharging, and resting plans on a general intercity or regional network where charging stations and rest stops are deployed. When traveling between their origins and destinations, EV drivers are assumed to determine their travel plans to minimize their individual travel cost composed of driving time, rest time, charging cost, and fatigue cost, while preventing their batteries from being exhausted. The equilibrium model is then formulated as a variational inequality and transformed into a nonlinear optimization problem. An efficient solution algorithm integrating column generation and Benders decomposition approach is proposed to solve the established optimization problem. Numerical examples are presented to demonstrate the performance of the proposed models and solution algorithm. Numerical results validate that considering the impact of driving fatigue on the travel cost emphasizes the need for en-route charging for EV drivers with long-distance trips, and has an appreciable impact on the network flow and charging demand distribution. In addition, large-sized batteries and fast chargers may not necessarily reduce drivers' travel costs for long-distance travel since charging behavior can be synchronized with drivers' resting behavior and thus contribute to the mitigation of drivers' fatigue.