Title: Moment analysis of highway-traffic clearance distribution,
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.