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A Review of Properties of Flow-Density Functions

机译：流量密度函数的性质综述

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Flow-density functions are often described as the fundamental relationship of traffic theory and are the basis of kinematic wave models or hydrodynamic models which are used to describe, predict or analyse traffic behaviour. We set out several different properties that it is generally agreed that flow-density functions should satisfy. We then take the many forms of flow-density functions that have been proposed or used over the past several decades, derive the properties of each one and consider whether, or to what extent, they satisfy each of the desirable properties. We find that few, if any, flow-density functions satisfy all of the desirable properties. The main reasons for this are that, in almost all cases, there are not enough independent parameters in the flow-density functions to capture all of the desirable properties and that, in almost all cases, the flow-density functions are specified as a single analytic function rather than a different function for each range of traffic behaviours, such as free-flow, congested and heavily congested traffic.
机译：流量密度函数通常被描述为交通理论的基本关系，并且是用于描述，预测或分析交通行为的运动波模型或流体动力学模型的基础。我们提出了几个不同的特性，这些特性通常都应满足流量密度函数的要求。然后，我们采用过去几十年来提出或使用的多种形式的流量密度函数，推导每个函数的特性，并考虑它们是否满足或满足每个期望的特性。我们发现很少有流量密度函数满足所有期望的特性。这样做的主要原因是，在几乎所有情况下，流量密度函数中没有足够的独立参数来捕获所有期望的特性，并且在几乎所有情况下，流量密度函数都被指定为单个分析功能，而不是针对各种流量行为（例如自由流量，拥塞和严重拥塞的流量）使用不同的功能。

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