## 2 Materials and Methods
At roundabouts where it was not possible to design the right roadway edge with radii R\({}_{\text{j}}\) and R\({}_{\text{j+1}}\)\({}^{\prime}\), the line from the center of the outer radius R\({}_{\text{o}}\) perpendicular to the trajectory of the vehicle's right turn movement was drawn (Figure 3b). Then, a circle of radius R\({}_{\text{o}}\)--u/2 was constructed from the R\({}_{\text{o}}\) center. Traffic stream conflicting points, exiting point (C) and entering point (C\({}^{\prime}\)), were defined as intersections of these entities. The distance between exiting and entering traffic streams along the center of the circulatory lane, i.e., the length of the circular arc between conflicting points b\({}_{\text{j}}\) was then measured. Figure 2: Roadway right edge design based on the trajectory of the vehicle’s right-turn movement: (a) defined by entry radius and exit radius; (b) defined by the trajectory of the design vehicle. Once designed, the geometric parameters \(R_{i}\), \(u\), \(e_{j}\), \(e_{j}^{\prime}\), and \(b_{j}\) were systematized according to the \(R_{o}\) and \(\delta\). When designing a roundabout according to the previously described procedure, it should be noted that the results depend on the experience and subjective approach of the designer. Therefore, to better present the influence of the chosen \(R_{o}\) and \(\delta\) on the designed parameters, regression analysis was performed, and best-fit curves with a coefficient of determination larger than 0.99 were created. Second-degree polynomial curves were used to describe \(R_{i}\) and \(u\) as a function of \(R_{o}\), and third-degree polynomial curves were used to describe \(e_{j}\), \(e_{j}^{\prime}\), and \(b_{j}\) as a function of \(R_{o}\) for different \(\delta\). Additionally, the average difference between \(b_{j}\) (\(j=1,2\), and \(3\)) for \(\delta=90^{\circ}\) and \(b_{j}\) (\(j=1,2\), and \(3\)) for \(\delta=85^{\circ},80^{\circ}\), and \(75^{\circ}\) was calculated. The entry degree of saturation (\(x_{mj}\)) was defined as the ratio of entering traffic flow and entry capacity. According to [14], sustainable values of \(x_{mj}\) range from 0.0 to 1.0 (values above 1.0 indicate an excess of entering traffic demand over entry capacity). \(x_{mj}\) was calculated for each designed scheme considering the following simplifications and assumptions on traffic flow volume, distribution, and composition:  
* Three travel directions through the roundabout were considered at each roundabout entry (\(j=1,\,\ldots,4\)): right turn, straight passage, and left turn (\(i=1,\,\ldots,12\)). * Traffic flow \(q_{i}\) at each entry (\(j=1,\,\ldots,\,4\)) in each travel direction (\(i=1,\,\ldots,\,12\)) was 150 veh/h, adding up to a total of 1800 veh/h passing through the roundabout (Figure 4a). * The influence of pedestrian and bicycle traffic on roundabout capacity was not considered. * The influence of heavy vehicles on the traffic flow quality was considered through the homogenization of traffic flows \(q_{i}\). Flat-rate conversions of each \(q_{i}\) from vehicles per hour (veh/h) to \(Q_{i}\) in passenger car units per hour (pcu/h) were made by using a conversion factor of \(f_{T}=1.1\), prescribed by [26] in case of lacking real data on flow composition: \[Q_{i}=f_{T}\cdot q_{i},\] (1) where \(Q_{i}\) is homogenized traffic flow in the direction \(i\) (pcu/h), \(f_{T}\) is conversion factor (set to 1.1), and \(q_{i}\) is traffic flow in the direction \(i\) (veh/h). Figure 3: Defining the distance \(b\) along the center of the circulatory lane, for roadway right edge design defined by the: (**a**) entry and exit radius; (**b**) design vehicle trajectory. The same procedure for determining the entering, exiting, and circulating traffic flows given in [26] was used for both the analytical and regression models. Based on assumed traffic conditions, 12 entering and exiting traffic flows \(\mathrm{Q_{i}}\) for each travel direction (i = 1,..., 12) were calculated.