Estimating the Mean Critical Gap

The estimation of the critical gap has been an issue since the 1970s, when gap acceptance was introduced to evaluate the capacity of unsignalized intersections. The critical gap is the shortest gap that a driver is assumed to accept. A driver's critical gap cannot be measured directly, and a number of techniques have been developed to estimate the mean critical gaps of a sample of drivers. This paper reviews the ability of the maximum likelihood technique and the probability equilibrium method to predict the mean and standard deviation of the critical gap with a simulation of 100 drivers, repeated 100 times for each flow condition. The maximum likelihood method gave consistent and unbiased estimates of the mean critical gap, whereas the probability equilibrium method had a significant bias that was dependent on the flow in the priority stream. Both methods were reasonably consistent, although the maximum likelihood method was slightly better. If drivers were inconsistent, again the maximum likelihood method was superior. A criticism leveled at the maximum likelihood method has been that a distribution of the critical gap has to be assumed. It was shown that this did not significantly affect the method's ability to predict the mean and standard deviation of the critical gaps. Finally, the maximum likelihood method can predict reasonable estimates with observations for 25 to 30 drivers. A spreadsheet procedure for using the maximum likelihood method is provided in this paper. The probability equilibrium method can be improved if the maximum rejected gaps are used.