报 告 人：金文龙 副教授
金文龙教授，1998年获得中国科学技术大学自动控制学士学位，2003年获得加州大学戴维斯分校（University of California, Davis）应用数学博士学位，现任加州大学尔湾分校（University of California, Irvine）土木与环境工程系副教授（Associate Professor）。现主要从事网络运动波理论、道路交通流理论、网联车系统理论、绿色驾驶策略等方面的研究。在Transportation Research Part B上发表论文30余篇。现任Transportation Research Part B编辑委员会编辑，IEEE Transactions on Intelligent Transportation Systems和Transportmetrica B副主编。
All existing day-to-day dynamics of departure time choice at a single bottleneck are unstable, and this has led to doubt over the existence of a stable user equilibrium in the real world. However, empirical observations and our personal driving experience suggest stable stationary congestion patterns during a peak period. In this paper we attempt to reconcile the discrepancy by presenting a stable day-to-day dynamical system for drivers' departure time choice at a single bottleneck. In our model, the decision variable in the execution stage is still drivers' departure times on the next day, but in the planning stage before the execution stage drivers determine their departure times in order to arrive at the destination at better times, with lower scheduling costs. We first define within-day traffic dynamics with the point queue model, costs, the departure time user equilibrium (DTUE), and the arrival time user equilibrium (ATUE). We then identify three behavioral principles in the planning stage: (i) Drivers choose their departure and arrival times in a backward fashion (backward choice principle); (ii) After choosing the arrival times, they update their departure times to balance the total costs (cost balancing principle); (iii) They choose their arrival times to reduce their scheduling costs or gain their scheduling payoffs (scheduling cost reducing or scheduling payoff gaining principle). In this sense, drivers' departure and arrival time choices are driven by their scheduling payoff choice. With a single tube or imaginary road model, we convert the nonlocal day-to-day arrival time shifting problem to a local scheduling payoff shifting problem. After introducing a new variable for the imaginary density, we apply the Lighthill-Whitham-Richards (LWR) model to describe the day-to-day dynamics of scheduling payoff choice and present splitting and cost balancing schemes to determine arrival and departure flow-rates accordingly. We define the scheduling payoff user equilibrium (SPUE) as the stationary state of the LWR model, formulate a new optimization problem for the SPUE, and prove the global stability of the SPUE and, therefore, ATUE and DTUE, by using Lyapunov's second method, in which the objective function in the optimization formulation is the potential function. We also develop the corresponding discrete models for numerical solutions and use one numerical example to demonstrate the effectiveness and stability of the new day-to-day dynamical model. Different from existing ones, the new adjustment mechanism leads to stable day-to-day departure time choice dynamics by guaranteeing that drivers have better choices of departure/arrival times with larger scheduling payoffs on the next day, and such better choices are not over-chosen due to the constraint imposed by the single tube's cross-section area, which is equal to the jam density in the LWR model. This study is the first step for understanding stable day-to-day dynamics for departure time choice, and many follow-up studies are possible and warranted.