Time headway variable and probabilistic modeling

Three types of probabilistic models are distinguished for time headway (TH) distribution in this paper: the single model, the combined model and the mixed model. To challenge the flexibility of the models, a sample set is established based on different sampling methods according to different data bases from the roadways in France. Particularly, the data from the RN118 national roadway are aggregated over 6 min and classified according to traffic flow and traffic occupancy. An estimation process is proposed for the existing estimation methods when calibrating combined and mixed models. As a result, the two mixed models, the gamma based Semi-Poisson Model and the gamma based Generalized Queuing Model (gamma-GQM) are shown to be statistically equivalent, provide the best fits in a wide range of TH samples. The gamma-GQM without location parameter is recommended to use in TH modeling. Besides, the Shifted Hyper Log-normal Model (HyperLNM) is examined for the first time and fits to TH data very well in many cases. The statistical role of the location parameter in TH models is also discussed. Moreover, it is found that the Ratio between time Headway and Instantaneous Speed (RHIS) can be modeled well using the gamma-GQM.

► Three types of time headway (TH) probabilistic models are distinguished. ► The Γ-GQM using the 3-step estimation process accompanied with the MLE is recommended. ► The HyperLNM is examined and its performance is confirmed for the first time. ► The statistical role of location parameter is studied in different TH models. ► The ratio between TH and instantaneous speed is well calibrated using the Γ-GQM.