## Proposed Approach
### Assumptions of the Roundabout Traffic Model  
The model was prepared so as to enable traffic flow simulation on a multi-lane roundabout with multiple entrance and exit roads. The model describes right-hand traffic. The lanes on the roundabout are numbered from 0 (inner lane) to \(n-1\), where \(n\) corresponds to the total number of lanes on the roundabout. The feeder road consists of the entrance road and the exit road. The right-hand lane of the entrance road and the right-hand lane of the exit road are to first lanes to be numbered starting from zero. The right-hand lane is the lane on the right-hand side from the point of view of a driver travelling on the road in the given direction. Due to different lengths of the roundabout lanes, it is impossible to divide them into the same number of cells. Assuming that the cell length is constant and amounts to 2.5 m, the outer lanes will have more cells than the inner ones, reflecting the actual differences in the lanes lengths. The lane length, taking its inner (shorter) edge, may be determined using the formula:  
\[l_{lane}=2\times\pi\times(r_{island}+n\times w_{lane}) \tag{1}\]  
where \(l_{lane}\) is the lane length, \(r_{island}\) is the island radius, \(n\) is the subsequent lane number, starting from the inner lane numbered 0, and \(w_{lane}\) is the single lane width. The developed model posits that the width of each lane \(w_{lane}\) is the same. By parameterising the model in relation to the actual size of the roundabout, the number of cells in each lane is determined in relation to its length:  
\[n_{cells}=\left\lfloor\frac{l_{lane}}{2.5}\right\rfloor \tag{2}\]  
The resulting value is rounded down, as the number of cells making up a lane must be an integral number. Assuming that the radius of a sample roundabout amounts to 28 m, and the lane width is 4.5 m, the number of cells on subsequent lanes will then be, respectively: \(n_{cells}=\left\lfloor\frac{2\times\pi\times(28\;m+0\times 4.5)}{2.5\;m} \right\rfloor=\left\lfloor 70.37\right\rfloor=70\) and \(n_{cells}=\left\lfloor\frac{2\times\pi\times(28\;m+1\times 4.5)}{25\;m} \right\rfloor=\left\lfloor 81.68\right\rfloor=81\). The outer lane will be divided into 81 cells, and the inner lane into 70 cells. Distance from the exit. If the cells in the roundabout lane are numbered with subsequent values from the range \(<0,\;c_{max}>\), the distance to the nearest exit \(d_{exit}\) may be computed using the formulas:  
\[d_{exit}=c_{exit}-c_{current}\;dla\;c_{current}\leq c_{exit} \tag{3}\]  
\[d_{exit}=c_{max}+1-\left|c_{exit}-c_{current}\right|\;dla\;c_{current}>c_{ exit} \tag{4}\]  
Distance from the entrance. As the cells in the entrance road are numbered with subsequent values from the range \(<0,\;c_{max}>\), the distance of the simulated vehicle from the entrance into the roundabout \(d_{entrance}\) equals the difference between the cell connected with the roundabout \(c_{entrance}\) and the cell currently containing the front of the vehicle \(c_{current}\). \[d_{entrance}=c_{entrance}-c_{current} \tag{5}\]  
Calculation of the cell value in the subsequent iteration for vehicles entering and exiting the roundabout is dependent on information on adjacent cells. Adjacent cells are those which link the feeder road with the roundabout internal road. Adjacency does not need to be of the first degree. For example, cells in the inner lane of the roundabout are not directly adjacent to any cell in the feeder road. However, there are cells located between the aforementioned cells which link the two lanes and enable movement of vehicles. When a vehicle exits the roundabout, an adjacent cell is the last one which the vehicle covers on its lane before moving into a cell located in the feeder road lane. Depending on the lane on which the vehicle is located and the lane onto which it is going to move, these will be different cells corresponding to the natural turns taken by vehicles.