Estimating Minimum Gap Acceptances for Merging Motorists

Abstract

Assume that motorists arrive at a stop sign and wish to merge into traffic on the main road, using the following criterion for making decisions: For each motorist there is a number, X, which is the smallest headway which the motorist will accept before merging into it. For each of these gaps presented to a particular motorist, X is the same, but X varies from motorist to motorist, and has the distribution function FX(x). Assuming the gaps are independent and identically distributed variates, and the merging motorists arrive at times independent of the traffic on the main road, consistent estimates of the moments of X are obtained, using sample values of the accepted and rejected gaps. An estimator of FX(x) is also obtained, without these assumptions. The paper concludes with a numerical analysis using data obtained from an intersection in Sydney.

Laboratory and field analyses of decisions involving risk.

“…An analysis of variance of the arcsine-transformed proportions yielded a significant main effect of sex for the within-intersection data, F(l, 7) = 14.59, p < .01. The tendency for females to be more conservative than males in various real-life driving situations has been found in a number of studies (e.g., Ebbesen & Haney, 1973;Leff & Gunn, 1973;McNeil & Morgan, 1968). In short, something about the simulation eliminated an otherwise strong sex effect.…”

A Note on the Analysis of Gap-Acceptance in Traffic

“…These estimates can then be used to replace the right-hand side of (6) and then a quadrature formula used to estimate fL. Table 2 illustrates the use of this method on some data collected in Sydney in 1965 by the present author; a sample of these data was used by McNeil and Morgan (1968) in their paper. The lags and gaps were measured to about 0·1 sec accuracy using tapeswitches across traffic lanes.…”

Development and Use of a Computer Simulation Model for the Evaluation of Design and Control Alternatives for Intersections of Minor Road with Multi-Lane Rural Highways: Selection of Simulation Model : Interim Report

“…In his study only one accepted or rejected gap was recorded for each minor road vehicle and the problem arising from the inclusion of multiple rejections was not considered. McNeil and Morgan's work (15) on the other hand, did consider the question of multiple rejections and alternative methods of estimating the critical gap distribution and its moment were developed according to whether the major road headway distribution is known or unknown.…”