For decades, vehicle time-headway distribution models have been studied by many researchers and traffic engineers. A good time-headway model can be beneficial to traffic studies and management in many aspects; e.g. with a better understanding of road traffic patterns and road user behaviour, the researchers or engineers can give better estimations and predictions under certain road traffic conditions and hence make better decisions on traffic management and control. The models also help us to implement high-quality microscopic traffic simulation studies to seek good solutions to traffic problems with minimal interruption of the real traffic environment and minimum costs. Compared within previously studied models, the mixed (SPM and GQM) mod- els, especially using the gamma or lognormal distributions to describe followers headways, are probably the most recognized ones by researchers in statistical stud- ies of headway data. These mixed models are reported with good fitting results indicated by goodness-of-fit tests, and some of them are better than others in com- putational costs. The gamma-SPM and gamma-GQM models are often reported to have similar fitting qualities, and they often out-perform the lognormal-GQM model in terms of computational costs. A lognormal-SPM model cannot be formed analytically as no explicit Laplace transform is available with the lognormal dis- tribution. The major downsides of using mixed models are the difficulties and more flexibilities in fitting process as they have more parameters than those single models, and this sometimes leads to unsuccessful fitting or unreasonable fitted pa- rameters despite their success in passing GoF tests. Furthermore, it is difficult to know the connections between model parameters and realistic traffic situations or environments, and these parameters have to be estimated using headway samples. Hence, it is almost impossible to explain any traffic phenomena with the param- eters of a model. Moreover, with the gamma distribution as the only common well-known followers headway model, it is hard to justify whether it has described the headway process appropriately. This creates a barrier for better understanding the process of how drivers would follow their preceding vehicles. This study firstly proposes a framework developed using MATLAB, which would help researchers in quick implementations of any headway distributions of interest. This framework uses common methods to manage and prepare headway samples to meet those requirements in data analysis. It also provides common structures and methods on implementing existing or new models, fitting models, testing their performance hence reporting results. This will simplify the development work involved in headway analysis, avoid unnecessary repetitions of work done by others and provide results in formats that are more comparable with those reported by others. Secondly, this study focuses on the implementation of existing mixed models, i.e. the gamma-SPM, gamma-GQM and lognormal-GQM, using the proposed framework. The lognormal-SPM is also tested for the first time, with the recently developed approximation method of Laplace transform available for lognormal distributions. The parameters of these mixed models are specially discussed, as means of restrictions to simplify the fitting process of these models. Three ways of parameter pre-determinations are attempted over gamma-SPM and gamma-GQM models. A couple of response-time (RT) distributions are focused on in the later part of this study. Two RT models, i.e. Ex-Gaussian (EMG) and inverse Gaussian (IVG) are used, for first time, as single models to describe headway data. The fitting performances are greatly comparable to the best known lognormal single model. Further extending this work, these two models are tested as followers headway distributions in both SPM and GQM mixed models. The test results have shown excellent fitting performance. These now bring researchers more alternatives to use mixed models in headway analysis, and this will help to compare the be- haviours of different models when they are used to describe followers headway data. Again, similar parameter restrictions are attempted for these new mixed models, and the results show well-acceptable performance, and also corrections on some unreasonable fittings caused by the over flexibilities using 4- or 5- parameter models.

Temps Inter-véhiculaire (TIV) est une variable microscopique fondamentale dans la théorie du trafic, et a été étudié depuis le début du développement de cette théorie, vers 1930. La distribution de probabilité du TIV décrit la répartition des arrivées des véhicules en un point donné et reflète dans une certaine mesure le comportement de conduite. Beaucoup d'applications en ingénierie du trafic viennent de la connaissance fine de cette variable. La thèse a pour but d'approfondir cette connaissance en modélisant la distribution du TIV dans différents contextes selon différents points de vue. Tout d'abord, deux méthodes d'échantillonnage, la méthode de groupement et la méthode de raffinement sont considérées. L'application numérique concerne deux bases de données, celle de la route nationale RN118 et celle de l'autoroute A6. Ensuite, trois types de modèles probabilistes sont analysés et classifiés. Une comparaison exhaustive des modèles et des méthodes d'estimation est réalisée ce qui conduit à considérer que le modèle gamma-GQM est supérieur aux autres modèles en matière de performance statistique et en efficacité de calcul. Différentes procédures d'estimation sont testées, celle qui est proposée et retenue favorise la stabilité des paramètres estimés. Six nouveaux modèles de TIV sont proposés, calibrés, analysés. Mis à part deux modèles de performance inférieure aux autres et au modèle gamma-GQM, quatre modèles sont équivalents voire meilleurs que le modèle gamma-GQM. Pour une raison pratique, le modèle Double Gamma est choisi à côté du modèle gamma-GQM, comme modèle de comparaison, dans toute la modélisation des TIV. Le calibrage des modèles et l'analyse des paramètres des modèles sont menés, à partir des données réelles, en considérant trois dimensions d'étude du trafic: les échelles macroscopique, mésoscopique et microscopique. Une quatrième dimension d'étude des TIV est constituée des facteurs exogènes au trafic. La prise en compte de ces facteurs exogènes, à chaque échelle macroscopique entraîne la distinction de deux types de facteur exogène : « empêchant » et « impulsant». Finalement, différentes approches de validation sont testées. L'approche proposée par « enveloppe des distributions » semble prometteuse pour le futur / Time Headway (TH) is a microscopic variable in traffic flow theories that has been studied since the 1930s. Distribution of this fundamental variable describes the arrival pattern of vehicles in traffic flow, so probabilistic modeling is the main approach to study TH and represent driving behaviour. The applications of the variable in traffic engineering are varied; include capacity calculation, microscopic simulation, traffic safety analysis, etc. This dissertation aims at modeling the TH distribution in different contexts. Firstly, the short-time sampling method and long-time sampling method are applied to obtain TH samples from the two data bases (the RN118 national roadway and the A6 motorway). Then, three probabilistic TH model types are analyzed and classified. An exhaustive comparison between the existing models and between the corresponding estimation methods lead to consider that the gamma-GQM is the best TH model in the literature. An estimation process is also proposed in order to obtain good and stable estimated results of the parameters. After that, the TH probabilistic modeling is developed by six new models. Except for the two ones which are worse, the four other models are statistically equivalent and/or better than the gamma-GQM. For practical reason, the Double Gamma model is selected, as a comparison model, with the gamma-GQM to calibrate all TH samples. Three traffic levels are considered: macroscopic, mesoscopic and microscopic. The effects of exogenous factors are also examined. Examining this factor in each macroscopic variable level leads to distinguish two following factor types: impeding factor and propulsive factor. Finally, different approaches for TH validation are tested. The proposed approach of “envelope of distributions” seems to be promising for future applications