Equilibrium of Probabilities for Estimating Distribution Function of Critical Gaps at Unsignalized Intersections

The critical gap is an important parameter for capacity analysis at unsignalized intersections. This parameter is stochastically distributed and cannot be obtained directly by field measurements. Thus, many procedures for estimating the critical gap have been developed. A new model for estimating critical gaps at unsignalized intersections was introduced. The new model used equilibrium of probabilities for rejected and accepted gaps and did not require presumptions regarding the distribution function of critical gaps and driver behavior. This new model has led to an unparameterized empirical distribution of critical gaps. The mathematical function of the critical gaps was not required in advance. A solution is presented to account for predefined distribution functions of critical gaps. Regression analysis is used to calibrate two distribution functions—lognormal distribution and Weibull distribution—to the empirical distribution of critical gaps. The Weibull distribution better represents the distribution of critical gaps.