This study is an attempt to establish a suitable speed–density functional relationship for heterogeneous traffic on urban arterials. The model must reproduce the traffic behaviour on traffic stream and satisfy all static and dynamic properties of speed–flow–density relationships. As a first attempt for Indian traffic condition, two behavioural parameters, namely the kinematic wave speed at jam (C_j) and a proposed saturation flow (λ), are estimated using empirical observations. The parameter C_j is estimated by developing a relationship between driver reaction time and vehicle position in the queue at the signalised intersection. Functional parameters are estimated using Levenberg–Marquardt algorithm implemented in the R statistical software. Numerical measures such as root mean squared error, average relative error and cumulative residual plots are used for assessing models fitness. We set out several static and dynamic properties of the flow–speed–density relationships to evaluate the models, and these properties equally hold good for both homogenous and heterogeneous traffic states. From the numerical analysis, it is found that very few models replicate empirical speed–density data traffic behaviour. However, none of the existing functional forms satisfy all the properties. To overcome the shortcomings, we proposed two new speed–density functional forms. The uniqueness of these models is that they satisfy both numerical accuracy and the properties of fundamental diagram. These new forms would certainly improve the modelling accuracy, especially in dynamic traffic studies when coupling with dynamic speed equations.

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异构交通数据的速度-密度函数关系：统计和理论研究

这项研究试图为城市动脉上的异构交通建立合适的速度-密度函数关系。该模型必须重现交通流上的交通行为，并满足速度-流量-密度关系的所有静态和动态属性。作为印度交通状况的首次尝试，使用经验观测值估算了两个行为参数，即堵塞时的运动波速（C _j）和拟议的饱和流（λ）。参数C _j通过在信号交叉口处的驾驶员反应时间和队列中车辆位置之间的关系建立估算值。使用R统计软件中实现的Levenberg-Marquardt算法估计功能参数。诸如均方根误差，平均相对误差和累积残差图之类的数字量度用于评估模型适用性。我们列出了流-速度-密度关系的一些静态和动态属性，以评估模型，这些属性对于同质和异质交通状态同样适用。从数值分析中发现，很少有模型能够复制经验速度-密度数据流量行为。但是，现有功能形式都无法满足所有特性。为了克服这些缺点，我们提出了两种新的速度密度函数形式。这些模型的独特之处在于它们既满足数值精度又满足基本图的特性。这些新形式肯定会提高建模精度，尤其是在与动态速度方程式耦合时进行动态交通研究时。