Dynamic User Equilibrium for Electric Vehicle Departure Time and Path–Charging Choices with Wireless and Fast Charging Services

Abstract

This study investigates how coordinated wireless and fast charging services reshape electric vehicle departure time and path–charging choices when a trip-level charging requirement must be completed before arrival. A multi-class dynamic user equilibrium model is formulated for road networks containing wireless charging lanes and fast charging stations. An energy-aware dynamic network loading model propagates traffic and battery states, transfers upstream wireless energy into the residual station workload, and determines endogenous waiting. The equilibrium is expressed as a finite-dimensional variational inequality and solved by an energy-aware inertial fixed-point framework with safeguarded route swapping and independent verification. Experiments on the Nguyen–Dupuis and Sioux Falls networks show that low-state-of-charge users depart 6.91 min earlier on average, while exposure-informed wireless-charging placement can substantially reduce downstream station waiting and exhibits saturation once all behaviorally exposed links are active. Under compound demand and low-state-of-charge pressure, roadway queues activate more sharply than station waiting. In a common Sioux Falls algorithm benchmark, the inertial method reaches stable acceptance in 776.2 s compared with 1562.9 s for its non-inertial counterpart. The method of successive averages crosses the practical gap threshold earlier but does not satisfy the common flow-stability criterion within 3000 updates and 9018.1 s. Across 30 final Sioux Falls scenarios, all solutions satisfy the practical verified gap and physical feasibility gates, with 11 difficult cases requiring explicit route-swap continuation. The results clarify the complementary operational roles of corridor and station charging while delimiting the numerical and behavioral assumptions of the framework.