Some Remarks Regarding the Estimation of Critical Gaps

Abstract

For the estimation of critical gaps for unsignalized intersection analysis, the so-called maximum likelihood method currently is treated as the best approach. This paper demonstrates that the maximum likelihood method is a special case of the more general mathematical survival theory for the estimation of interval-censored parameters. The assumption of a special mathematical type for the statistical distribution of critical gaps is an essential part of the method. Test applications with various types of functions show that the results do not significantly depend on the applied type of distribution. Therefore, the traditional lognormal distribution is not an essential part of the theory. Instead, it is reasonable to apply that type of distribution that can be handled more easily. From this standpoint, the logistic distribution is favorable. Because the variance of each kind of distribution of the critical gaps does not contribute to the precision of the result, a simplified method is useful if the standard deviation of the critical gaps can be predefined and if only the scale parameter of the function is adjusted to the measured gap data. The results from this single-parameter method are rather congruent with those from the more complicated two-parameter method. The simplified approach opens the way to apply critical gap estimation in traffic engineering practice to adjust capacity calculations to local driver behavior.