基于基本图分段仿射逼近的扩展蜂窝传输模型PWA-CTM

F. Alimardani, J. Baras
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引用次数: 0

摘要

在过去的几十年中,广泛使用的一阶细胞传输模型(CTM)的许多不同版本被提出用于最优交通控制。公路交通管理技术,如匝道计量(RM),通常是基于非线性约束的优化问题设计的,这些约束源于基本图(FD)的流密度关系。大多数扩展的CTM版本都是基于基本图(FD)的流密度关系的梯形近似,试图简化优化问题。然而,这种关系本质上是非线性的,粗糙的近似会极大地影响优化解的效率。在本研究中,我们提出了一类基于流量密度关系的分段仿射近似的扩展ctm,这样(a)与真实关系相关的积分平方误差与梯形近似相比大大减少,并且(b)优化问题对于匝道计量最优控制器的实时应用仍然易于处理。采用两步识别方法用分段仿射函数逼近FD,得到我们所说的PWA-CTMs。所提出的模型通过最优匝道计量控制器的性能进行评估,例如使用广泛使用的PI-ALINEA方法,在复杂的公路交通网络中。仿真结果表明,与其他CTM扩展相比,基于pwa -CTM的优化问题所需的计算时间更少,同时可以获得更高的流量和密度演化精度。因此,所提出的PWA-CTMs构成了一阶交通流模型的最佳近似方法之一,可用于更一般和更具挑战性的建模和控制应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
PWA-CTM: An Extended Cell-Transmission Model based on Piecewise Affine Approximation of the Fundamental Diagram
Throughout the past decades, many different versions of the widely used first-order Cell-Transmission Model (CTM) have been proposed for optimal traffic control. Highway traffic management techniques such as Ramp Metering (RM) are typically designed based on an optimization problem with nonlinear constraints originating in the flow-density relation of the Fundamental Diagram (FD). Most of the extended CTM versions are based on the trapezoidal approximation of the flow-density relation of the Fundamental Diagram (FD) in an attempt to simplify the optimization problem. However, this relation is naturally nonlinear, and crude approximations can greatly impact the efficiency of the optimization solution. In this study, we propose a class of extended CTMs that are based on piecewise affine approximations of the flow-density relation such that (a) the integrated squared error with respect to the true relation is greatly reduced in comparison to the trapezoidal approximation, and (b) the optimization problem remains tractable for real-time application of ramp metering optimal controllers. A two-step identification method is used to approximate the FD with piecewise affine functions resulting in what we refer to as PWA-CTMs. The proposed models are evaluated by the performance of the optimal ramp metering controllers, e.g. using the widely used PI-ALINEA approach, in complex highway traffic networks. Simulation results show that the optimization problems based on the PWA-CTMs require less computation time compared to other CTM extensions while achieving higher accuracy of the flow and density evolution. Hence, the proposed PWA-CTMs constitute one of the best approximation approaches for first-order traffic flow models that can be used in more general and challenging modeling and control applications.
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