Measuring Critical Gap

A method is derived which estimates the probability distribution of the critical gaps of those drivers entering a main road at a priority junction who have rejected the initial lag offered to them, using observations of the sizes of the gaps refused and that eventually accepted by the driver. An extension of the method estimates the probability distribution of the critical times of all drivers, on the assumption that each driver’s critical lag and critical gap are equal, from observations of the sizes of the initial lags accepted and rejected by the driver, and the sizes of subsequent gaps considered if the initial lag is rejected. Both methods have been tested using data obtained by computer simulation. Estimates of the mean and standard deviation obtained using each method are substantially unbiased and have a fairly small standard error. Estimates of the critical gap and critical time distributions obtained using the methods are subject to considerable errors in individual cells of the distribution, however, unless the data set used is very large. An approximate method is also suggested whereby the original probability distribution of the critical gap of all drivers, including those who accept the initial lag, can be estimated from the same data by assuming a simple form for any difference between the distributions of critical lags and critical gaps.