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

PDF (DX094490.pdf) - White Rose Etheses Online

## 80 However, the values

80 However, the values he reports are not strictly comparable to the ones in this study as they refer to the entrance as a whole. related by He does suggest, though, that the two parameters are in = 0.45c + 0.16 which he rounds up to C = 2m According to this a = (2m+) = 2+- 2m = tJber (1978) considered the behaviour of queues of turning vehicles moving into large gaps at a T-junction controlled by a STOP sign. The relationship he derived between N and T is based on the median start-up times of the first and subsequent vehicles making a left turn and the median remainder rejected lag: N = 0.29T - 0.74 (eq. 4.10) Cooper and Wennell (1978) proposed two models which they call "the direct linear relationship" and "the explanatory model" respectively. Both models are developed to describe a merging and a crossing manoeuvre. Only the merging relationships are mentioned here.

81 The direct linear relationship is T = 2.8N + 4.9 (eq. 4.11) The explanatory model takes the form T = S+N.M+R (eq. 4.12) where S: median start-up time (sec) M: median move-up time (sec) R: median residual gap (sec) This relationship becomes T = 3.ON + 3.0 (eq. 4.13) for the merging manoeuvre they were studying. The T consider the explanatory model more useful as it enables the effect of changes in the individual components of queue acceptance on the overall relationship to be evaluated. Considering equations 4.9, 4.10, and 4.11 it is of interest to note that Cooper and Wennell interchange the dependent and independent variables. Instead of treating T as the independent variable they assume it is the dependent variable. They regard T as inappropriate to be the independ- ent variable for the data they were using, since they are sampled from continuous distributions of gap sizes for fixed, integer, values of N. They also comment on the applicability of the term "regression" for such models. They note that the distribution of the lengths of gaps accepted by a given number of vehicles is markedly skew, i.e. there is always a larger number of gaps at the lower values of the range. This is contrary to the

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