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# PDF (DX094490.pdf) - White Rose Etheses Online

PDF (DX094490.pdf) - White Rose Etheses Online

## 64 Cooper et al (1977),

64 Cooper et al (1977), Wennell and Cooper (1981) ). Other distributions used were the shifted negative exponential (Herman and Weiss (1961), McNeil and Morgan (1962), Blumenfeld and Weiss (1979) ), the Erlang distribution (Blunden et al (1962) ), and the Pearson Type III (Gamma) distribution (Drew (1967) ). McNeil and Morgan (1968) have developed a method of building up a distribution from the available data rather than fitting a theoretical model on the data. One problem associated with the inclusion of all offered gaps in the acceptance probability distribution has been the bias introduced by the inclusion of comparatively more rejections by drivers with large critical gaps. This inclusion results in critical gap values larger than the true values. To avoid this bias, Greenshield et al (1947) included in their analysis, only the lags whereas Blunden et al (1962) used an equal number of accepted and rejected gaps by first assuming that all gaps larger than the one accepted by a driver would also be accepted and that all gaps shorter than the ones he rejected would also be rejected,and then factoring the latter to equalise the two totals. Drew (1967) used only the accepted gaps and the largest rejection of each driver. Ashworth (1968, 1970) quantified the bias, assuming a fixed critical gap for each driver, and proposed as the corrected median critical gap, the following = m -s 2 q (eq.4.1) where in: the median value of the observed gap acceptance distribution (sec) s 2 : the variance of the observed gap acceptance distribution (sec2)

65 have been developed that use more complex descriptions than Tanner's formulae. These models usually assume that the critical gap follows some distribution between drivers rather than assume a single value for ct. The analysis of the data pro- vides a measure of the mean or median and of the variance of this distribution. In the following sections some of these methods of analysis will be presented. It should be noted that all the methods included in sections 4.2.1 - 4.2.4 provide a measure of the critical gap only. The present study was interested in methods estimating both the critical gap and move-up time parameters. These methods are described in sections 4.3 and 4.4 in more detail. 4.2.1 The Critical Gap as the Median of a Distribution Most methods suggested are variations of the one introducted by Greenshields et al (1947). Here only the lags offered were considered and the percentage acceptance of each size group was determined. A lag is defined as the time interval between the arrival of the side road vehicle at the stop line and the passage of the next major road vehicle. Their method defined the critical lag as the one with 50% probability of being accepted. Since then other researchers have used all available data in the acceptance distribution, i.e. both offered lags and gaps. A number of different theoretical distributions have been fitted to the data to obtain the median value. The most common distributions applied were the normal distribution (Worrall et al (1967), Ashworth (1968, 1969, 1970), Ashworth and Bottom (1977), Powell and Glen (1978) ) and the l 0 ;-normal distribution (Solberg and Oppenlander (1966), Wagner (1966), Ashton (1971),

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