Exploring the uncertainty in capacity estimation at roundabouts

Purpose In gap-acceptance theory the critical and the follow up headways have a significant role in determining roundabout entry capacities which in turn depend on circulating flow rates under a specified arrival headway distribution. Calculation considers single mean values of the gap-acceptance parameters, neglecting the inherent variations in these random variables and providing a single value of entry capacity. The purpose of this paper is to derive the entry capacity distribution which accounts for the variations of the contributing (random) variables and suggest how to consider this issue in the operational analysis of the roundabouts. Methods We performed a Monte Carlo simulation to get the distribution of entry capacity and found Crystal Ball software effective for performing the random sampling from the probability density functions of each contributing parameter. A steady-state model of capacity was used for performing many runs; in each run, the values of each contributing parameter were randomly drawn from the corresponding distributions. Results The paper presents the first simulations and the entry capacity distributions at roundabouts, once the probability distributions of the headways were assumed. The results of the analysis were expressed probabilistically, meaning that the probability distributions of capacity rather than the simple point estimates were obtained. Conclusions Comparing the capacity values based on a meta analytic estimation of critical and follow-up headways and the capacity functions based on the probability distributions of the model parameters, more insights in developing an appropriate approach to capacity estimation at roundabouts can be gained.