## 3 Results  
The results of the roundabout geometric design showed that to simultaneously fulfill two roundabout design conditions (regarding preferred arc length and the roundabout's right roadway edge design, Table 3) values of \(\mathrm{R_{o}}\) for different \(\delta\) should be (1) \(\mathrm{R_{o}}\geq\) 13.5 m for \(\delta=85^{\circ}\), (2) \(\mathrm{R_{o}}\geq\) 16.5 m for \(\delta=80^{\circ}\), and (3) \(\mathrm{R_{o}}\geq\) 19.0 m for \(\delta=75^{\circ}\). Considering the fulfillment of the abovementioned conditions (Table 3), designing a roundabout with a \(\delta\leq 75^{\circ}\) is not recommended. However, the roundabout design that does not consider these two design conditions could be applied in the suburban environment because of the spatial limitations. Therefore, calculations of the \(\mathrm{x_{mj}}\) were performed for all 60 designed roundabouts, based on the calculated traffic flow volumes shown in Figure 7.  
The resulting values of the geometric parameters of the 60 designed roundabouts schemes are shown with their best-fit curves in Figures 8, 9a, 10, 11 and 12a. As shown in Figure 8, \(\mathrm{R_{i}}\), \(\mathrm{e_{i}}\), \(\mathrm{e_{i}}^{\prime}\), and \(\mathrm{b_{j}}\) were proportional to \(\mathrm{R_{o}}\), and \(\mathrm{u}\) values were inversely proportional. The change in \(\mathrm{e_{i}}\) was (1) proportional to \(\delta\), (2) identical for \(\delta=90\) and \(85^{\circ}\), (3) identical for \(\delta=80\) and \(75^{\circ}\) at \(\mathrm{R_{o}}=13.0\) m, and (4) identical for \(\delta=90\), \(85\), and \(80^{\circ}\) at \(\mathrm{R_{o}}\geq 19.0\) m. The change in \(\mathrm{e_{2}}\) was inversely proportional to \(\delta\) at \(\mathrm{R_{o}}\geq 14.0\) m. The change in \(\mathrm{e_{2}}^{\prime}\) and \(\mathrm{e_{3}}^{\prime}\) at \(\mathrm{R_{o}}\geq 16.0\) m showed an uneven trend for different \(\delta\). As expected, \(\delta\) did not affect the entrance and exit widths e\({}_{3}\), e\({}_{4}\), \(\mathrm{e_{1}}^{\prime}\), and \(\mathrm{e_{4}}^{\prime}\). As shown in Figures 9a, 10, 11 and 12a, the trend of \(\mathrm{b_{j}}\) increasing for different \(\delta\) corresponded to those of \(\mathrm{e_{j}}\) and \(\mathrm{e_{j}}^{\prime}\). Thus, the change in \(\mathrm{b_{1}}\) (1) was proportional to \(\delta\) and (2) was identical for \(\delta=90\) and \(85^{\circ}\). The change in \(\mathrm{b_{2}}\) was inversely proportional to \(\delta\) at \(\mathrm{R_{o}}\geq 14.0\) m. \(\delta\) had a negligible effect on the values of \(\mathrm{b_{3}}\) at \(\mathrm{R_{o}}<16\) m. The change in \(\delta\) had no effect on the values of \(\mathrm{b_{4}}\). Extreme values of \(\mathrm{b_{j}}\) were observed for \(\delta=75^{\circ}\) and \(\mathrm{R_{o}}=13.0\) m (\(\mathrm{b_{1}}=12.5\) m) at leg 1, and \(\mathrm{R_{o}}=20.0\) m (\(\mathrm{b_{2}}=25.7\) m) at leg 2. Figure 7: Calculated values of entering, exiting, and circulating traffic flow in \(\mathrm{pcu/h}\). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \(\mathrm{R_{o}}\) (m) & **13.0** & **13.5** & **14.0** & **14.5** & **15.0** & **15.5** & **16.0** & **16.5** & **17.0** & **17.5** & **18.0** & **18.5** & **19.0** & **19.5** & **20.0** \\ \hline \(\delta=90^  
Figure 8: Geometric parameters \(\mathbf{R}_{i}\), \(\mathbf{e}_{j}\), \(\mathbf{e}_{j}^{\prime}\), and u as a function of \(\mathbf{R}_{o}\) for different \(\delta\). Figure 10: Investigated parameters at leg 2 as a function of \(\mathrm{R_{o}}\) for different \(\delta\), considering the application of design conditions 1 and 2: (**a**) geometric parameter \(\mathrm{b_{2}}\); (**b**) traffic parameter \(\mathrm{x_{m2}}\). Figure 9: Investigated parameters at leg 1 as a function of \(\mathrm{R_{o}}\) for different \(\delta\), considering the application of design conditions 1 and 2: (**a**) geometric parameter \(\mathrm{b_{1}}\); (**b**) traffic parameter \(\mathrm{x_{m1}}\).