The traffic flow analysis and the relevant vehicle distribution ("free-moving" or "platooned" vehicles)
IntroductionThe traffic flow composition and the relevant presence of vehicle platoons is particularly interesting in traffic study, and more generally in Highway Engineering, with reference to a plethora of theoretical and practical applications. For instance, as for "traffic operations" [1][2][3][4], it is well known how the presence of platoons can influence breakdown probability [5,6]. Moreover, platoon analyses turned out to be important also in the study of car accidents and road safety [7]. Such a very high practical interest accounts for the numerous models developed over the years. By way of an example, it is worth mentioning the research conducted by Baras et al. [8], which also considers facilities with interrupted flow -and the most recent studies by Ramezani et al. [9] and Jiang et al. [10]. Still today, therefore, the topic has a remarkable scientific and practical interest and deserves in-depth analysis.At first, this article briefly describes the Pearson type III distribution which represents a time headway probability model (more specifically, a generalized mathematical model). The peculiarity of the Pearson type III distribution is its capacity to generate distribution families depending on the chosen model parameters, which can be suited to a plethora of types of traffic phenomena. In the course of this research, some of the above formulations were used to analyse a vehicle distribution within a traffic flow in steady-state conditions and notably to identify the presence and composition of vehicle platoons. In order to apply this analysis to a great number of observations, a specific algorithm was designed and calibrated according to empirical surveys, suitable to randomly simulate a traffic flow and to "identify" the essential characteristics of any present vehicle platoon. The algorithm was implemented to generate realizations of the random function Q(t) (i.e. a traffic flow on a road cross-section in function of time t) starting from input data. The resulting random functions were properly studied and their main characteristics (i.e. non-random functions: mathematical hope and variance) were determined to confirm the steady state flow hypothesis assumed for the development of this study.