70 that the simplified

70 that the simplified models (1) and (2), compared with models (3) and (4) respectively, lead to an accurate estimate of the true average delay, a slightly overestimated probability of no delay (highway transparency) and capacity of the minor• road, and seriously overestimated variance of delay. 4.2.5 The Move-Up Time, Tanner (1962, 1967) uses, in his capacity and delay formulae, the parameter which is defined as the time between successive vehicles accepting the same gap. According to this theory a gap, T, would be accepted by one vehicle if it is equal or greater than the critical gap, a, i.e. if T ^ a, by two vehicles if T ^ a ^ .$, and by n if T ^ a + .(n-l)B. The estimation of the move-up time has not received the same attention as the critical gap. In general the value of has been assumed to be constant in the theoretical models of gap-acceptance, although a few researchers have proposed a specific move-up time for each position in the queue of entering vehicles. In most cases the value of has been abstracted as the mean of the observations of the extra time that vehicles in the queue after the leading one need to accept the same gap (Bendtsen (1972), Uber (1978), Powell and Glen (1978)).Cooper and Wennell (1978) used the median of the distribution. Armitage and McDonald (1974) chose the value of such that when the critical gap is calculated, by a modified Raff method, the two together have the effect that the total observed entries are equal to the total number of entries predicted from the same gap data. Pearson and Ferreri (1961) and Worrall et al (1967) built cumulative acceptance distributions for the extra time used by subsequent vehicles in

71 a merging platoon. Although they do not report any values as the move-up time or by any other definition, Worrall et al conclude that there is no significant difference among the acceptance distributions for the second, third, and fourth vehicles in line in a multiple merge. See Fig. 4.4 for an example of the acceptance probability curves. Bendtseri (1972) gives different values for the second, third, fourth and any subsequent vehicle which are progressively smaller, 4.2, 3.9, 3.8, 3.7 sec respectively. Uber (1978) gives the following values for the same vehicles 3.54, 3.53, 3.74 and 4.10 sec. Cooper and Wennell (1978) report values for the second, third and any subsequent vehicles, which were 2.9, 3.2, 2.9 sec respectively. The last three studies were conducted at priority T-junctions. Powell and Glen (1978) studied gap acceptance at roundabouts. They arrived at one value for all vehicles in a multiple acceptance. However, they suggested different values for the various types of roundabouts they studied. The values they suggest ranged from 2.0 to 3.3 sec. It is of interest to note that some roundabout capacity models proposed by Wohi and Martin (1967), Ashworth and Field (1973) and Ashworth and Laurence (1975) assume the move-up time to be equal to the critical gap. The methods discussed in the following sections provide values for both gap-acceptance parameters simultaneously. 4.3 The Work of Armitage and McDonald Armitage and McDonald conducted a series of studies