基于Logistic曲线的交通流速度-密度关系建模

Modeling of Speed-density Relationship in Traffic Flow Based on Logistic Curve

为了解析交通流速度与密度关系,推导出了一组交通流参数物理意义明确且符合交通流特性的通用Logistic模型。从Logistic模型本质出发,讨论速度变化率的表达形式,结合交通流实际情况修正速度变化率并引入速度上确界概念,建立了一系列Logistic模型;通过改变取值,给出了模型参数变化对Logistic速度-密度曲线的影响,并细致讨论了参数的物理意义及获取方法;最后分别采集区段和断面的全交通状态数据进行模型验证。结果表明:模型3对2组数据的拟合优度分别为0.931 3和0.970 4,该模型能够很好地描述不同状态下的交通流特性。

In order to characterize the speed-density relationship in traffic flow, a group of generalized logistic models were proposed with physically meaningful and explicit parameters, which can fit field data well. Starting from the initial concept of Logistic model, the expression of speed change rate was discussed in detail, and thus three models were derived by modifying the change rate of speed and introducing the supremum of speed. The influences of parameters on logistic speed-density curve were provided by changing one parameter each time while keeping the others fixed, and the physical meaning of parameters and the acquisition method were discussed in detail. Both section data and fixed-location data were validated for the practicality. The result shows that the goodness of fit of model 3 for the two groups of date is 0. 931 3 and 0. 970 4 respectively, and the proposed model characterize the speed-density relationship well under various traffic states.