Moment Analysis of Highway-Traffic Clearance Distribution

Abstract

Abstract-To help with the planning of inter-vehicular communication networks, an accurate understanding of traffic behavior and traffic phase transition is required. We calculate inter-vehicle spacings from empirical data collected in a multi-lane highway in California, USA. We calculate the correlation coefficients for spacings between vehicles in individual lanes to show that the flows are independent. We determine the first four moments for individual lanes at regular time intervals, namely the mean, variance, skewness and kurtosis. We follow the evolution of these moments as the traffic condition changes from the low-density free flow to high-density congestion. We find that the higher moments of inter-vehicle spacings have a well defined dependence on the mean value. The variance of the spacing distribution monotonously increases with the mean vehicle spacing. In contrast, our analysis suggests that the skewness and kurtosis provide one of the most sensitive probes towards the search for the critical points. We find two significant results. First, the kurtosis calculated in different time intervals for different lanes varies smoothly with the skewness.They share the same behavior with the skewness and kurtosis calculated for probability density functions that depend on a single parameter. Second, the skewness and kurtosis as functions of the mean intervehicle spacing show sharp peaks at critical densities expected for transitions between different traffic phases.The data show a considerable scatter near the peak positions, which suggests that the critical behavior may depend on other parameters in addition to the traffic density.

Model-based assessment of the impact of driver-assist vehicles using kinetic theory

“…Interestingly, such a fat-tailed trend has been found in some experimental data on the headway distribution in highway traffic, cf. [1], and related to the presence of high occupancy vehicles in the traffic stream. Moreover, the standard deviation of the normalised distribution 1 ρ f ∞ (s), which, from the known formulas for the statistical moments of inverse Gamma random variables, is s d (ρ)/ √ 1 + 2p, depends linearly on the mean headway s d (ρ), a fact which is in turn reported as an experimental observation in [1].…”

“…We address this issue by means of the following result: Lemma 4.2. Let S ∈ R + be the random variable expressing the equilibrium headway of any vehicle from its leading vehicle, with probability density function 1 ρ f ∞ , cf. (24).…”

Data Transmissions Using Hub Nodes in Vehicular Social Networks

“…Our model assumes that inter-vehicle distances (or intervehicle headways) are Poisson (exponentially) distributed. An excellent and recent analysis of this topic is in [41], including several references in which empirical data were used to confirm that the exponential model is generally a good fit for the distributions of inter-vehicle distances. Furthermore, several papers have used exponential distribution for modelling the inter-vehicle distances [42], [43], [44].…”

Connectivity analysis of directed highway vehicular ad hoc networks using graph theory

“…Without losing generalization, we limit our study to free‐flowing traffic. This is mainly because in free‐flow traffic phase ( ρ < 25 vehicle/km), 60,61 the headway distances are large compared to those associated with congested traffic. In congested traffic regimes, the close distances between vehicles guarantee that they fall within the communication range of one another; in such regimes, the interference becomes a problem, but this falls outside the scope of this article.…”