Derivation of Capacity Equation for Roundabout Entry with Mixed Circulating and Exiting Flows

Abstract

A gap acceptance model for roundabouts that takes the proportion of exiting vehicles into account was developed. Exiting vehicles are assumed to influence the gap acceptance process in the following way: when they leave the roundabout, new gaps that consist of combinations of old gaps arise. The distribution of the new gaps is obtained by a convolution of the distribution of the old gaps. It is shown that the proportion of exiting vehicles can have a strong effect on the entry capacity of a minor stream. The effect depends on where the exiting point is situated, which in turn depends on the ability of the minor-stream driver to detect an exiting vehicle. The model attaches greater importance to the proportion of exiting vehicles than the macro models do. This can partly be explained by an erroneous placement of the exiting point. The model has various implications for the measurement of critical gaps. If the proportion of exiting vehicles is large, critical gaps will be overestimated because of the failure to take into account the minor-stream vehicles that are waiting for exiting vehicles.