Parametric modeling of the heteroscedastic traffic speed variance from loop detector data

Abstract

Traffic speed variance is defined as a measure of the dispersion of space mean speeds among drivers. Empirical speed-density observations exhibit a structured traffic speed variance, which has been found to be associated to the roadway crash rate, the fatality rate, and travel time variability. The objective of this paper is to propose a generalized traffic speed variance function to describe this structured variance. The proposed speed variance function is a response of the speed-density curve with two additional parameters. The estimation of the model parameters in the proposed traffic speed variance function can be carried out through an iterative nonlinear least-square algorithm (i.e., LevenbergMarquardt). A series of logistic speed-density curve with varying parameters are used in the proposed traffic speed variance function with different levels of performance. The proposed traffic speed variance model can potentially help to unveil the underlying mechanism of empirical traffic phenomenon such as spontaneous congestion or capacity reduction.Judging from the empirical observations of traffic speed variance in the previous section, we found that these two variance functions are not appropriate to model a parabola-shaped variance function. 285HETEROSCEDASTIC TRAFFIC SPEED VARIANCE in the speed-density curve and its corresponding variance function can be estimated by a least-square iterative procedure (this paper used the leastsq in scipy.optimize [27]). To evaluate the performance of the proposed traffic speed variance models, the authors will compare the 3PL, 4PL, and 5PL speed-density models to the empirical mean of a speed-density observation; simultaneously, the authors also compare the traffic speed variance functions based on the 3PL, 4PL, and 5PL models to the empirical traffic speed variances as can be seen from the left half in Figures 11 and 12. The EM represents the empirical mean of the scattered speed-density observation, whereas EV is the empirical traffic speed variance at this location. Similarly, the nPL (n = 3, 4, 5) represents the mean curve estimated from the n-parameter logistic speed-density models. On the right-hand side of Figures 11 and 12, the MR indicates the mean residual, which is the difference between the empirical mean and the mean Figure 11. Performance of the three-parameter, four-parameter, and five-parameter logistic speed-density models against the empirical mean and residuals between their corresponding variance models and empirical variance at station 4001119 and 4001120. 292H. WANG ET AL.

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