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（AssociateProfessor）。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 TransportationSystems和TransportmetricaB副主编。
Allexisting day-to-day dynamics of departure time choice at a single bottleneckare unstable, and this has led to doubt over the existence of a stable userequilibrium in the real world. However, empirical observations and our personaldriving experience suggest stable stationary congestion patterns during a peakperiod. In this paper we attempt to reconcile the discrepancy by presenting astable day-to-day dynamical system for drivers' departure time choice at a singlebottleneck. In our model, the decision variable in the execution stage is stilldrivers' departure times on the next day, but in the planning stage before theexecution stage drivers determine their departure times in order to arrive atthe destination at better times, with lower scheduling costs. We first definewithin-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 behavioralprinciples in the planning stage: (i) Drivers choose their departure andarrival times in a backward fashion (backward choice principle); (ii) Afterchoosing the arrival times, they update their departure times to balance thetotal costs (cost balancing principle); (iii) They choose their arrival timesto reduce their scheduling costs or gain their scheduling payoffs (schedulingcost reducing or scheduling payoff gaining principle). In this sense, drivers'departure and arrival time choices are driven by their scheduling payoffchoice. With a single tube or imaginary road model, we convert the nonlocalday-to-day arrival time shifting problem to a local scheduling payoff shiftingproblem. After introducing a new variable for the imaginary density, we applythe Lighthill-Whitham-Richards (LWR) model to describe the day-to-day dynamicsof scheduling payoff choice and present splitting and cost balancing schemes todetermine arrival and departure flow-rates accordingly. We define thescheduling payoff user equilibrium (SPUE) as the stationary state of the LWRmodel, formulate a new optimization problem for the SPUE, and prove the globalstability of the SPUE and, therefore, ATUE and DTUE, by using Lyapunov's secondmethod, in which the objective function in the optimization formulation is thepotential function. We also develop the corresponding discrete models fornumerical solutions and use one numerical example to demonstrate theeffectiveness and stability of the new day-to-day dynamical model. Differentfrom existing ones, the new adjustment mechanism leads to stable day-to-daydeparture time choice dynamics by guaranteeing that drivers have better choicesof departure/arrival times with larger scheduling payoffs on the next day, andsuch better choices are not over-chosen due to the constraint imposed by thesingle tube's cross-section area, which is equal to the jam density in the LWRmodel. This study is the first step for understanding stable day-to-daydynamics for departure time choice, and many follow-up studies are possible andwarranted.