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

PDF (DX094490.pdf) - White Rose Etheses Online

## 102 Roundabout were

102 Roundabout were analysed to provide both a counting and a headway distribution. The results are shown in Tables 4.26 and 4.27. The data from Moore Street Roundabout were analysed to provide just a counting distribution, see Table 4.28. The observed distributions were examined to establish if the simpler theoretical models, i.e. the Poisson counting, the negative exponential and the shifted negative exponential distributions could be used. Using the observed headway distribution for the Castle Square data the value of k in the Erlang distribution was derived. In that distribution k is given by k - (mean)2 variance The mean of the distribution was 3.42 sec, the standard deviation 3.15 sec, and the variance 9.92 sec2. - 3.422 - 11.696 - k - 9.92 - 9.92 - 1.179 When this value is rounded to the nearest integer k became 1 and the Erlang distribution was reduced to the negative exponential. It should also be noted that the ratio (mean! standard deviation) equalled 1.086, which is very close to unity. - The observed counting distributions were examined to establish if the data, when grouped into fifteen second intervals, are random. Each data point representing the number of arrivals per 15 sec interval was regressed on the corres- ponding value for the immediate previous 15 sec interval. For the data to be random, with 95% conficience, the correlation

103 coefficient of the regression should lie within the range ±1.96 , where n is the number of pairs of data points. The v/n results of the regressions are given in Table 4.29. As can be seen the hypothesis for either roundabout cannot be rejected. The above analysis suggests that the use of the Poisson counting distribution and either the simple or the shifted negative exponential interval distribution is suitable for the traffic conditions observed. The data were therefore compared with theoretical distributions using the X 2 -test. The two observed counting distributions were first compared to the theoretical Poisson counting distribution. In neither case was the observed distribution rejected at the 5% level, (see Tables 4.30 and 4.31). However, it was found that the headway distribution at Castle Square Roundabout could not be accepted as similar to either a theoretical negative exponential distribution or a shifted negative exponential distribution with t = 0.27 sec (see Table 4.32). (The figure of 0.27 sec was arrived at as the difference of the mean and the standard deviation of the observed distribution and gives a theoretical distribution having the same mean and variance as the observed distribution of headways). Since the analysis so far had proved inconclusive in suggesting a suitable value for T, it was decided to use the simulation program to produce headways based on a shifted negative exponential distribution. The value of the shift, t, was input to the simulation together with the other flow characteristics. The value of T was varied from 0.0 to 1.0 sec and the circulating flow used was the value obtained at

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