As electric vehicle (EV) penetration increases, the mixed traffic of EVs and gasoline vehicles (GVs) will be prevalent in roadway systems for a long time. Meanwhile, EV incentive policies, adjusted adaptively as a response to EV market growth, will perturb the mixed traffic pattern periodically. Such periodic perturbation will cause mixed traffic to evolve from disequilibrium to a new equilibrium. This equilibration is theoretically indeterminate due to the non-uniqueness of mixed traffic equilibria and the dynamic interaction between operational policy and underlying mixed traffic. The non-unique mixed-traffic equilibrium in the previous period influences the traffic stationary state and traffic evolution trajectory in the next period, which is also non-unique. Thereby, the indeterminacy in the equilibration process affects the long-term mixed traffic performance that should be factored into the period-to-period adjustment of EV incentive policies. This effect calls for the study of mixed traffic equilibration as a theoretical foundation for long-term policymaking, which has not received significant attention. This paper explores the properties of mixed traffic equilibria and proposes a mixed traffic evolution model considering time-varying EV penetration. The mixed traffic evolution model is then integrated into a control framework to support the period-to-period adjustment of EV-promoting tolling policy. Numerical examples illustrate the effects of non-unique mixed traffic equilibria and period-to-period toll adjustment schemes on long-term mixed traffic performance.

随着电动汽车 (EV) 普及率的提高，电动汽车和汽油车 (GV) 的混合交通将在道路系统中长期普遍存在。同时，为响应电动汽车市场增长而进行适应性调整的电动汽车激励政策将定期扰乱混合交通模式。这种周期性扰动会导致混合交通从不平衡演变为新的平衡。由于混合流量均衡的非唯一性以及运营策略与潜在混合流量之间的动态交互，这种均衡在理论上是不确定的。前一时期的非唯一混合交通均衡影响下一时期的交通静止状态和交通演化轨迹，也是非唯一的。从而，平衡过程中的不确定性影响长期混合交通性能，应考虑到电动汽车激励政策的逐期调整。这种效应需要研究混合交通均衡作为长期决策的理论基础，但尚未受到重视。本文探讨了混合交通均衡的特性，并提出了一种考虑时变电动汽车渗透率的混合交通演化模型。然后将混合交通演化模型集成到控制框架中，以支持电动汽车推广收费政策的周期调整。数值例子说明了非唯一混合交通平衡和周期收费调整方案对长期混合交通性能的影响。