The Morning Commute Problem with Carpool and Dynamic Toll Scheme

This study extends the bottleneck model to analyze dynamic user equilibrium (UE) in carpooling during the morning peak commute. It is assumed that the carpooling platform offers both traditional human-driven vehicles and novel shared autonomous vehicles. First, we analyze the traffic distribution on a two-lane road. We find that traffic distribution is influenced by the additional cost of carpooling behavior. A corresponding functional relationship is established and visualized. Second, we derive the critical fare threshold for carpooling. Carpooling occurs only when the fare is below this threshold. Third, we obtain the user equilibrium (UE) solution under a specified case, including flow distribution, equilibrium cost, and total number of vehicle. Furthermore, a system-optimal dynamic tolling scheme is proposed to minimize total system cost while maintaining commuter UE. By equating the system marginal cost to the equilibrium cost, we derive the analytical expression for the lane toll function. Numerical experiments demonstrate that the toll scheme effectively reduces the total system cost. We find that when the average occupancy rate of carpooling vehicles exceeds a certain threshold, both the user equilibrium cost and total number of vehicles for commuters are shown to decrease. This indicates that more people will choose carpooling. Additionally, the impact of shared autonomous vehicle (SAV) penetration in carpooling fleets on the overall system is examined. We find that an increase in SAV penetration rate has a positive impact at the system level. This research provides insights into the influence of SAV on traditional carpooling services and proposes traffic management strategies tailored to such scenarios, offering new perspectives for conventional traffic management approaches.