Estimation of Parameters in Distribution of Headways in Roundabouts

Estimation of parameters in the distribution of headways in roundabouts is a cumbersome task. Inherent to data employed are temporal variation together with dependence between successive vehicles. This is a consequence of the sampling period and interactions in the roundabouts. The elimination of observations, so as to obtain trend-free samples of independent vehicles, removes too much information from the data. If all the observations are used, the results of the parameter estimations are affected by temporal variation and dependence between headways. In this paper, an analysis of the statistical properties of the headways between major stream vehicles in roundabouts is described. The properties investigated were the existence of temporal variation in the measured headways and independent and identically distributed successive headways, i.e., if the headways were from a random sample. More than 50% of the investigated subsets suffered from trends or other nonrandom variations. The question whether these subsets should be excluded or not is discussed. Three methods for the estimation of parameters in the M3 distribution were tested. For the two-lane subsets, it was possible to demonstrate a linear relationship between the proportion of free vehicles and the volume. For the one-lane subsets, the adjusted $R^2$ was low, and the linear constant was not significant. Nevertheless, the distributions estimated by use of the two-lane subsets did not provide a better fit to the observed data than the distributions estimated by the use of one-lane subsets. The predicted capacity for a minor lane, i.e., the capacity obtained by the fitted distribution, was close to the capacity obtained by the empirical distribution function (the estimated capacity).