On an Interlocking Flexible Car Use Restriction Policy: Theory, Learning and Experiment

Car use restrictions, such as the commonly implemented license plate restriction policy (PRP), are regarded as effective strategies for alleviating traffic congestion in many cities worldwide. Although these regulations help reduce daily vehicle volumes and evenly distribute them, they also limit commuters’ freedom to choose when to drive. A recent flexible car use restriction policy (FRP) allows commuters to select specific days to refrain from using their cars within a restriction cycle, enhancing travelers’ flexibility in urgent situations. Although the original FRP (O-FRP) may incur slightly higher average driving costs compared with the PRP due to uneven car use distribution, it can ultimately lower overall travel costs by accommodating more car uses during emergencies. This study introduces an interlocking FRP (IL-FRP), which groups travelers and assigns them different restriction cycles starting from distinct weekdays. Theoretical analysis reveals that, even under relaxed nonlinear travel cost assumptions, the user equilibrium solution of the IL-FRP, under ideal conditions, converges with the system optimal solution and further reaches the FRP’s theoretical lower bound while minimizing both driving and transit costs. Additionally, we develop two IL-FRP variants that are applicable regardless of the urgency probability distribution: the equally grouped FRP (ILE-FRP) and the arbitrarily grouped FRP (Arb-FRP). To derive equilibrium solutions for all FRPs under different parameter settings, we present a three-step learning algorithm using the mean field game framework. Numerical experiments validate the effectiveness of this algorithm and demonstrate that IL-FRP, ILE-FRP, and Arb-FRP offer advantages over O-FRP in terms of total travel cost. A series of laboratory experiments was conducted to support our theoretical findings. The results indicate some bounded rationality among individuals but align consistently with our theoretical predictions and learning outcomes.