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PDF (DX094490.pdf) - White Rose Etheses Online

PDF (DX094490.pdf) - White Rose Etheses Online

86 the pattern of the

86 the pattern of the circulating flow repeats itself after 16384 gaps. The actual simulated time thus depends on the circul- ating flow. The accepted gaps were divided in groups of limited number (see section 4.5.7 on sample size effects). Each group was then analyzed and the gap-acceptance parameters calculated: Below the following aspects of the analysis are discussed 1. The use of rejected gaps, (section 4.5.3). 2. The effect of extreme values, (section 4.5.4). 3. The use of weights in the model, (section 4.5.5). 4. The definition of dependent and independent variables, (section 4.5.6). 5. The effect of sample size, (section 4.5.7). 6. The use of variable gap characteristics as input to the simulation, (section 4.5.8). Finally section 4.6 compares the overall performance of the models tested. Throughout the section the notation used is N, for the nuniber of vehicles accepting a gap, and T, the length of the gap. 4.5.3 The Use of Rejected Gaps As mentioned in section 4.3, Arinitage and McDonald included only the rejected gaps greater than L, the lost time. The data on which the analysis is performed have such dis- tributions that the number of gaps will always be disprop- ortionally larger at the value N = 0, i.e. for no acceptances, than at all other values of the dependent variable. This. influencesthe slope and the intercept of the linear model. The effect of excluding the rejected gaps was tested by analyzing sets of simulated data with and without

87 the rejected gaps. The results of the analysis are shown in the table below. The table shows the results from two 'sets of input values for the gap-acceptance parameters input values predicted values predicted values for simulation with rejected gaps without rejected gaps (i) : 2.25 3.33 2.40 c: 4.27 3.51 3.84 (ii) : 2.25 3.03 2.49 c: 3.99 3.36 3.45 It can be seen that for both sets of data the predictions were improved when the rejected gaps were not included in the analysis. As expected, the most marked improvement was for the value of , which is the reciprocal of the 1ope of the straight line. The above results also point to a feature that was observed consistently throughout the study of the linear model, i.e. the predictions for were always in much better agreement with the input values than the predictions for . The explanation can be that the value of c. is obtained by extrapolating outside the range of the used data to find the intercept, while is related directly to the slope of the linear model. Finally, the inclusion of rejected gaps would, obviously, use a larger part of the collected data since accepted gaps tend to be in a minority position in relation to the total number of gaps available. However, abstracting the data (e.g. from video tapes) involves considerable labour which is disproportionally increased if the rejected gaps are required. It is interesting to note in this respect, that

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