Disorderly traffic streams are those that, simply stated, do not have parallel lines (or lanes) of vehicles but have vehicles distributed more haphazardly in the road space. Vehicles in such streams, while moving longitudinally, change their lateral positions frequently. Their trajectories have a more pronounced wander along the width or the lateral dimension as opposed to those vehicles that primarily move in lanes. This property of disorderly streams dictates that its mathematical models must admit two spatial dimensions (the longitudinal and the lateral). Further, the observed impact of road geometry features like width, curvature, etc., on stream behavior, irrespective of whether the stream is disorderly, also suggests that realistic models of traffic streams must describe the streams using two spatial dimensions. Unfortunately, most of the theories of traffic dynamics are one-dimensional—they only consider the longitudinal dimension. This paper, while describing many of the existing approaches to modelling vehicular traffic behavior builds a case for strengthening two-dimensional modelling approaches that are all, still in their infancy. Given the (1) large increase in computation and data handling capabilities over the last decade and (2) significant strides made in developing tools for observing traffic dynamics at scales and accuracy levels that were previously unimaginable, the authors believe the time has come to develop, calibrate and validate reasonable two-dimensional models of traffic dynamics.

中文翻译：

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理解和建模无序交通流

无序交通流，简单地说就是没有平行的车辆线（或车道），但车辆在道路空间中分布更随意。在这样的溪流中，车辆在纵向移动时，经常改变它们的横向位置。与主要在车道上移动的车辆相比，它们的轨迹在宽度或横向尺寸上有更明显的漂移。无序流的这种特性决定了它的数学模型必须承认两个空间维度（纵向和横向）。此外，观察到的道路几何特征（如宽度、曲率等）对流行为的影响，无论流是否无序，也表明交通流的现实模型必须使用两个空间维度来描述流。很遗憾，大多数交通动力学理论都是一维的——它们只考虑纵向维度。本文在描述了许多现有的车辆交通行为建模方法的同时，为加强二维建模方法提供了一个案例，这些方法都还处于起步阶段。鉴于 (1) 在过去十年中计算和数据处理能力的大幅提高以及 (2) 在开发以前无法想象的规模和精度水平上观察交通动态的工具方面取得了重大进展，作者认为现在是时候发展了，校准和验证合理的交通动态二维模型。虽然描述了许多现有的车辆交通行为建模方法，但为加强二维建模方法提供了一个案例，这些方法仍处于起步阶段。鉴于 (1) 在过去十年中计算和数据处理能力的大幅提高以及 (2) 在开发以前无法想象的规模和精度水平上观察交通动态的工具方面取得了重大进展，作者认为现在是发展的时候了，校准和验证合理的交通动态二维模型。虽然描述了许多现有的车辆交通行为建模方法，但为加强二维建模方法提供了一个案例，这些方法仍处于起步阶段。鉴于 (1) 在过去十年中计算和数据处理能力的大幅提高以及 (2) 在开发以前无法想象的规模和精度水平上观察交通动态的工具方面取得了重大进展，作者认为现在是时候发展了，校准和验证合理的交通动态二维模型。