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PDF (DX094490.pdf) - White Rose Etheses Online

PDF (DX094490.pdf) - White Rose Etheses Online

90 vehicles than larger

90 vehicles than larger ones. Two weights were suggested, one for each distribution: W = for the negative exponential distribution f(t) = qt and q(t_T ____) W = e l-qT for the shifted negative exponential distribution f(t) = ---- etT'tT) t-T where W: the weight q: the flow (veh/sec) t: the size of the gap (sec) f(t): the probability density function (eq. 4.13) (eq. 4.14) (eq. 4.15) (eq. 4.16) 'r: the minimum headway of the circulating flow (sec) E: 1/q (sec/veh) As the circulating flow in the simulation program was assumed to have a shifted negative exponential distribution the weight applied was eq. 4.15. Tables 4.5 and 4.6 contain the results of weighted analysis of simulation data based on two sets of initial values. They contain results from analysing the data using two definitions of dependent/independent variables. The means and standard deviations of the predictions over all the groups are included in Table 4.7. All four predictions are satisfactory, while the definition of number of entries as dependent variable gave better predictions in set (i), and the

91 definition of gap size as dependent variable resulted in better predictions for set (ii) of the initial values. The predictions of the follow-up time, , are in much better agreement with the input values than the predictions of the critical gap, ct. Similarly the standard deviations associated with the mean of are less than half of the standard deviations associated with CL. This indicates that the confidence associated with the prediction of individual groups is less for the critical gap than the move-up time. The importance of this fact is that observed data collected at a half period during the peak period are likely to be less than 500 accepted gaps which is the number included in each of the groups analysed here (see section 4.5.7) 4.5.6 Dependent and Independent Variables Previous research on gap-acceptance, which has proposed linear models, has not determined the optimum definition of dependent and independent variables. Pearson and Ferreri, tJber, Armitage and McDonald assume the number of vehicles accepting a gap, N, as the dependent variable while Cooper and Wennell, Maher and Dowse prefer the gap size, T, as the dependent variable (see sections 4.3 and 4.4). Some justifications for using T as the dependent variable are included at section 4.5.1. Therefore it was decided to test both definitions. Tables 4.8, 4.9. 4.10. 4.11 and 4.12 include the results of using both definitions, both weighted and unweighted analysis. Table 4.7 contains the mean and standard deviations using weighted analysis only. As mentioned in the previous

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