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首页> 外文期刊>Transportation Research Part B: Methodological >Dynamic user equilibrium based on a hydrodynamic model
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Dynamic user equilibrium based on a hydrodynamic model

机译：基于水动力模型的动态用户平衡

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In this paper we present a continuous-time network loading procedure based on the Light-hill-Whitham-Richards model proposed by Lighthill and Whitham (1955) and Richards (1956). A system of differential algebraic equations (DAEs) is proposed for describing traffic flow propagation, travel delay and route choices. We employ a novel numerical apparatus to reformulate the scalar conservation law as a flow-based partial differential equation (PDE), which is then solved semi-analytically with the Lax-Hopf formula. This approach allows for an efficient computational scheme for large-scale networks. We embed this network loading procedure into the dynamic user equilibrium (DUE) model proposed by Friesz et al. (1993). The DUE model is solved as a differential variational inequality (DV1) using a fixed-point algorithm. Several numerical examples of DUE on networks of varying sizes are presented, including the Sioux Falls network with a significant number of paths and origin-destination pairs (OD). The DUE model presented in this article can be formulated as a variational inequality (VI) as reported in Friesz et al. (1993). We will present the Kuhn-Tucker (KT) conditions for that VI, which is a linear system for any given feasible solution, and use them to check whether a DUE solution has been attained. In order to solve for the KT multiplier we present a decomposition of the linear system that allows efficient computation of the dual variables. The numerical solutions of DUE obtained from fixed-point iterations will be tested against the KT conditions and validated as legitimate solutions.
机译：在本文中，我们提出了一种基于Lighthill和Whitham（1955）以及Richards（1956）提出的Light-hill-Whitham-Richards模型的连续时间网络加载过程。提出了一种微分代数方程组（DAEs）系统，用于描述交通流的传播，行进延迟和路线选择。我们采用一种新颖的数值装置将标量守恒定律重新构造为基于流的偏微分方程（PDE），然后使用Lax-Hopf公式进行半解析求解。这种方法可以为大型网络提供有效的计算方案。我们将此网络加载过程嵌入到Friesz等人提出的动态用户平衡（DUE）模型中。 （1993）。使用定点算法将DUE模型解决为差分变分不等式（DV1）。给出了不同大小的网络上DUE的几个数值示例，包括具有大量路径和起点-终点对（OD）的Sioux Falls网络。如Friesz等人报道，本文中提出的DUE模型可以表述为变分不等式（VI）。 （1993）。我们将介绍该VI的Kuhn-Tucker（KT）条件，该条件是任何给定可行解的线性系统，并使用它们来检查是否已达到DUE解。为了解决KT乘数，我们提出了线性系统的分解，该分解允许有效地计算对偶变量。从定点迭代获得的DUE的数值解将针对KT条件进行测试，并被验证为合法解。

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