## 1 Introduction
They have established relationships between capacity and geometric design features through statistical multivariate regression analyses to fit mathematical relationships between measured entry capacity, circulating flow, and other independent variables that have an impact on entry capacity [9; 14]. They consider not only the circulating and entering but also the exiting traffic flow. The relationship between entry capacity and circulating flow is linear or exponential, depending on the model [8; 11]. Simulation models are based on modeling the movements and interactions of individual vehicles on a network consisting of links and nodes or connectors. Vehicle movements are governed by gap acceptance, car-following, lane-changing, and other models, and are typically calculated for each vehicle at every specified time step [8]. In recent years, vehicle movements along a roundabout have been studied within the master equation formalism for stochastic exclusion processes of many-particle systems, i.e., many-body interactions. The finite dimensions of vehicles introduce a natural \"quantization\" of space, and developed models simulate the stochastic motion of particles (vehicles) along a roundabout through the (totally) asymmetric exclusion process [17; 18]. Although designers and analysts would like to perform estimations as completely and correctly as possible, model performance in predicting roundabout entry capacities is limited [19]. Even today, the discussion between analytical and regression models characterizes the general situation regarding the estimation of entry capacity at roundabouts [9; 12]. The main issues address the fact that both roundabout geometric parameters and traffic characteristics (volume, vehicle composition, and driver behavior) vary widely across the world [20]. However, according to [10; 21], geometric parameters have a much stronger impact on roundabout entry capacity than geographic location or country of origin, i.e., \"regional\" non-geometric driver behavior. Additionally, among the different factors influencing entry capacity, only the geometric parameters of roundabouts can be quantified and modified, i.e., entirely manipulated by the designers to improve roundabouts' operational performance [11]. The two objectives of the research presented in this paper are to (1) analyze and compare the results of roundabout performance estimations derived from analytical and regression models, and (2) quantify the model results' susceptibility to changes in roundabout geometric parameters. The investigation will be performed on 60 four-legged single-lane roundabouts schemes, varying in size and leg alignment, designed according to the results of the chosen design vehicle swept path analysis. The roundabout performance estimations will be performed under the assumption that the entering traffic at each leg is distributed in three travel directions through the roundabouts, in equal shares. To compare the results of the analytical and regression models, the roundabout entry degree of saturation will be calculated. This is a dimensionless value used as the intersection efficiency indicator in both models. The results of this research will reduce the uncertainty in decision-making during the final roundabout design stage.