Logistic modeling of the equilibrium speed–density relationship

Wang, Haizhong; Li, Jia; Chen, Qian-Yong; Ni, Daiheng

doi:10.1016/j.tra.2011.03.010

Cited by 87 publications

(85 citation statements)

References 18 publications

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“…For Wang et al [8] 3PL Model, though the above calibrating models with weight w 1 are almost the best calibrating models, the calibrating Wang et al [8] 3PL Model with weight w 1 with significance 0.05 cannot be obtained according to calculation, nor are the two calibrating models with weights w 2 and w 3 . For these calibrating models with LSM, weights w 1/3 and w 1/2 , are all similar, especially when the density is less than 50 veh/km.…”

Section: Resultsmentioning

confidence: 97%

“…For the Underwood Model, the density of the lowest precision of calibrating model using LSM in terms of RE is between 60 veh/km and 70 veh/km; for the Newell [7] Model, the density of lower precision of calibrating models using LSM in terms of RMSEs is between 30 veh/km and 40 veh/km, and more than 90 veh/km; for Wang et al [8] 3PL Model, the density of the lowest precision of calibrating models using LSM in terms of RMSE is between 80 veh/km and 90 veh/km. Different weight determination methods can change these conditions, for Underwood Model, the density of the lowest precision of calibrating model with weight w 3 in terms of RE is between 10 veh/km and 20 veh/km; for the Newell [7] Model, the density of lower precision of calibrating models with weight w 3 in terms of RMSEs is between 20 veh/km and 30 veh/km; for Wang et al [8] 3PL Model, the density of the lowest precision of calibrating models with weight w 1/3 in terms of RMSE is between 30 veh/km and 40 veh/km. Then, according to both REs and RMSEs under different conditions, the different best observation weight method is determined.…”

Section: Resultsmentioning

confidence: 99%

“…The results indicated that different models have different best calibrating models, for the Greenberg [5] Model, the calibrating model with weight w 1 is the best one, so are Underwood Model and Northwestern Model; for the Newell [7] Model, both calibrating models with weights w 1 and w 2 are the best ones; for Wang et al [8] 3PL Model, the best one is the calibrating model with weight w 1/2 , of which the calibrating models with weights w 2 and w 3 cannot be computed. This paper has confirmed that the calibrating models using LSM cannot reflect the speed-density relationship under congested/jam conditions and the results indicated that different speed-density models need to use different weight determination methods and not the weight w 1 only.…”

Section: Resultsmentioning

confidence: 99%

“…The original Georgia State Route 400 (GA400) ITS data were aggregated every 5 minutes, which were often used to generate the fundamental diagrams [8]. GA400 is a controlled-access state highway in the northern part of the US state of Georgia and the data were collected from a section with four lanes for one direction.…”

Section: Observation Data Informationmentioning

confidence: 99%

“…Several models including single-regime and multiple-regime ones were proposed by researchers. Greenshields et al [4] according to limited observations established the over-simplified linear model; Greenberg [5] developed a model by treating the traffic stream as a continuous fluid and the model turned out to be suitable for the traffic flow theory; Underwood thought that the exponential relationship between the negative density and speed could be used in free-flow conditions and the Northwestern Model is similar but a little more complicated than the Underwood model [6]; Newell [7] considered the non-linear effects in the dynamics of car following and obtained a special model; Wang et al [8] developed the logistic model of speed-density relationship motivated by the success of the generalized logistic curves in modelling the growth pattern phenomenon such as population dynamics, plant growth in agriculture, epidemic growth in biology, and market growth in economics. Besides, some multiple-regime models were also developed by Edie [9], Sun and Zhou [10], etc.…”

Section: Introductionmentioning

confidence: 99%

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Determination of Observation Weight to Calibrate Freeway Traffic Fundamental Diagram Using Weighted Least Square Method (WLSM)

Zhang¹,

Guo²,

Xi³

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Section: Resultsmentioning

confidence: 97%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Observation Data Informationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Determination of Observation Weight to Calibrate Freeway Traffic Fundamental Diagram Using Weighted Least Square Method (WLSM)

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Guo²,

Xi³

2017

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Data mining using regularized adaptive B‐splines regression with penalization for multi‐regime traffic stream models

Sun

Pan

2013

J of Advced Transportation

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SUMMARYThis paper presents a new data mining method that integrates adaptive B-spline regression and traffic flow theory to develop multi-regime traffic stream models (TSMs). Parameter estimation is implemented adaptively and optimally through a constrained bi-level programming method. The slave programming determines positions of knots and coefficients of the B-spline by minimizing the error of B-spline regression. The master programming model determines the number of knots through a regularized function, which balances model accuracy and model complexity. This bi-level programming method produces the best fitting to speed-density observations under specific order of splines and possesses great flexibility to accommodate the exhibited nonlinearity in speed-density relationships. Jam density can be estimated naturally using spline TSM, which is sometimes hardly obtainable in many other TSM. Derivative continuity up to one order lower than the highest spline degree can be preserved, a desirable property in some application. A five-regime B-spline model is found to exist for generalized speed-density relationships to accommodate five traffic operating conditions: free flow, transition, synchronized flow, stop and go traffic, and jam condition. A typical two-regime B-spline form is also explicitly given, depending only on free-flow speed, optimal speed, optimal density, and jam density.

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

Wang

Hurwitz

et al. 2013

J of Advced Transportation

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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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Logistic modeling of the equilibrium speed–density relationship

Cited by 87 publications

References 18 publications

Determination of Observation Weight to Calibrate Freeway Traffic Fundamental Diagram Using Weighted Least Square Method (WLSM)

Determination of Observation Weight to Calibrate Freeway Traffic Fundamental Diagram Using Weighted Least Square Method (WLSM)

Data mining using regularized adaptive B‐splines regression with penalization for multi‐regime traffic stream models

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

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