稳定的日常动态，用于出发时间选择
Stable day-to-day dynamics for departure time choice
摘要：
在本文中，我们提出了一个稳定的日常动力系统的司机出发时间选择在一个单一的瓶颈。我们首先定义了一天内的交通动态与点队列模型，成本，出发时间用户平衡（DTUE），和到达时间用户平衡（ATUE）。然后，我们确定了三个行为原则：（一）司机选择他们的出发和到达时间在一个落后的方式（逆向选择原则）;（ii）在选择到达时间后，他们更新出发时间以平衡总成本（成本平衡原则）;（iii）他们选择到达时间以降低调度成本或获得调度收益（调度成本降低或调度收益增加原则）。从这个意义上说，司机的出发和到达时间的选择是由他们的调度收益选择。利用单管或假想道路模型，将非局部的日到达时间转移问题转化为局部调度收益转移问题。在引入一个新的变量的虚密度，我们应用Lighthill-Whitham-Richards（LWR）模型来描述日常的动态调度支付选择和目前的分裂和成本平衡计划，以确定相应的到达和离开流量率。我们还发展了相应的离散模型的数值解。我们从理论上证明了LWR模型的日常平稳状态导致调度支付用户均衡（SPUE），这是等价于DTUE和ATUE和稳定。我们用一个数值例子来证明新的日常动力学模型的有效性和稳定性。
英文摘要：
In this paper we present a stable day-to-day dynamical system for drivers' departure time choice at a single bottleneck. 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: (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 also develop the corresponding discrete models for numerical solutions. We theoretically prove that the day-to-day stationary state of the LWR model leads to the scheduling payoff user equilibrium (SPUE), which is equivalent to both DTUE and ATUE and stable. We use one numerical example to demonstrate the effectiveness and stability of the new day-to-day dynamical model.
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