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PDF (DX094490.pdf) - White Rose Etheses Online

PDF (DX094490.pdf) - White Rose Etheses Online

92 section, this did not

92 section, this did not allow a conclusive decision. Table 4.13 includes the results for the same sets of initial values but for unweighted analysis. The predictions overall are worse than the ones of weighted analysis. However, standard deviations are much lower. Comparing the results of the two definitions, the results of analysis using the gap size (T) as the dependent variable are much better. The conclusion of these two sections is that best mean values are provided by weighted analysis while the standard deviation associated with the mean values is much smaller for unweighted analysis which assumes T as the dependent variable. 4.5.7 Effect of Sample Size - Another point investigated was the effect of reducing the sample size on the predictions and especially on the standard deviation of the mean over all the groups. The groups up to now consisted of 500 accepted gaps. However during a half-hour observation period the accepted gaps are usually much less. The groups of one set were divided up to form groups Of 200 vehicles. Table 4.14 shows the results. Table 4.15 is a collection of the respective results for a sample size of 500 vehicles. Comparison of the results shows that the reduction in sample size affected the prediction only by 0.01 sec while it increased the standard deviation by only a very small amount. Therefore the predictions based on a sample size of 200 are not significantly worse than those based on a sample size of 500.

93 4.5.8 The Effect of Assuming the Gap Characteristics not Constant Up to now the simulation assumed that cx and are the same for all drivers. This simplifying assumption was replaced by defining distributions of values for both the parameters. The distribution used was normal in each case. The simulation was carried out only for one set of initial values. Each entry vehicle was assigned its own critical gap and move-up time with the restricticn that no value should be outside the following range m + 2s > x ^ in - 2s where m is the input mean and s the input standard deviation. The accepted gaps were divided into 20 groups of 500 acceptances each. The analysis was performed as described previosuly. Tables 4.1 and 4.17 show the results of this set of simulation data. The predictions compare with the input values equally well as the predictions for constant cx and The standard deviation of the mean, however, is slightly larger than in the previous cases. (Compare Table 4.17 with Tables 4.14 and 4.15.) The increase is very small and does not invalidate the method when a and vary between drivers. 4.6 Comparison of the Simple Linear Model and Armitage and McDonald's Two-line Model As has been described in section 4.3, Armitage and McDonald have proposed a model which fits two straight lines to the data. This model is only slightly more complicated to apply once the data have been abstracted but requires the abstraction of rejected gaps. The simple linear model requires

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