Can day-to-day dynamic model be solved analytically? New insights on portraying equilibrium and accommodating autonomous vehicles

This paper develops a new approach to portray the equilibrium and analyze the appropriate lane policy during different deployment stages of autonomous vehicles (AVs) by innovatively integrating Vickrey's bottleneck model into the day-to-day dynamic model. The travel cost function in the classical bottleneck model is described by considering the impact of AVs' value of time (VOT) reduction and AV gain. The evolution of lane choice behaviors is described using the first-order and second-order day-to-day dynamic model. Furthermore, three lane policies are proposed to accommodate AVs' development, and the properties for the endogenous market penetration of AVs and travel cost under three lane policies are examined to recognize which policy is more suitable at different development stages of AVs. The results demonstrate that such equilibrium solutions as traffic flow, total travel cost, the convergence time are all analytically solvable and thus can perfectly answer the problem of stability and convergence involved in the day-to-day dynamic model. Finally, the numerical analysis is conducted to verify the previous findings and get some intuitive insights on system performance. This work not only provides new insights on the evolutionary process of AVs' and regular vehicles (RVs)' lane choice behaviors, but also recognizes appropriate lane policy to accommodate AVs from a novel perspective.