Modeling and Estimation of Headway Distributions

Abstract

A simple analysis to derive Branston’s generalized queueing model for (time-) headway distributions is presented. It is assumed that the total headway is the sum of two independent random variables: the empty zone and the free-flowing headway. The parameters of the model can be used to examine various characteristics of both the road (e.g., capacity) and driver-vehicle combinations (e.g., following behavior). Furthermore, the model can be applied to vehicle generation in microscopic simulation models and to safety analysis. To estimate the different parameters in the model, a new estimation method is proposed. This method, which was developed on the basis of Fourier-series analysis, was successfully applied to measurements collected on two-lane rural roads. The method was found to be both computationally less demanding and more robust than traditional parameter techniques procedures, such as maximum likelihood. In addition, the method provides more accurate results. Parameters in the model were examined with the developed estimation method. Estimates of these parameters at a specific period and a specific measurement location were to some extent transferable to other periods and locations. Application of the method to road capacity estimation is discussed.

Variations in Parameters of Time Headway Models According to Macroscopic Variables, Fundamental Diagram, and Exogenous Effects

“…The two methods have the common drawback of dividing data into classes and hence have difficulty establishing an effective estimation process. A method proposed by Hoogendoorn that uses Fourier transformation of the CDF of TH distribution was also tested (6). Per the comparison in Kolmogorov-Smirnov (K-S) statistic distance between the different estimation methods applied to many TH samples, the MLE that uses a three-step estimation process has been shown to be the most consistent, effective, and strongly proposed (3).…”

“…where g, G indicate the PDF and CDF, respectively, of the following TH U. Parameter λ represents the intensity of the exponential tendency, whereas θ is the participating part of the following vehicles. The distribution g of the following TH is subjectively assumed in advance and possibly depends on the driver's perception of traffic or environment (6). Hence, the gamma-GQM is the GQM that uses gamma-distribution as the g function.…”

Assessment of Roadway Capacity Estimation Methods

“…For a recent application of the headway model we refer to Hoogendoorn (1996). In this study, traffic measurements at two-Iane rural roads in the Netherlands were used to assess an improved method for parameter estimation of Branstons headway model.…”

Effects of edge rate of the designed line markings on the following time headway

“…It is distance headway, bumper to bumper distance between two consecutive vehicles in a lane, divided by the speed of the following vehicle. Generally, carfollowing models are built to obtain the distribution and evaluation of time headway [8][9][10][11]. Thus, it can easily be seen that the drivers' judgments of speed and distance are the main factors in the control of time headway.…”