## 4 Methods
### Connecting Alternative Networks-Through the Example of Large Vehicle Modelling
To characterize the fit between a given traffic flow and the grid under consideration, we define the ratio (\(\theta\)) of the nominal area demand of the given traffic flow (\(A_{F}-\) area used by the examined traffic flow according to the classical traffic engineering approaches) to the total area of the elementary regions actually assigned to the traffic flow by the system (\(Sum_{e}A_{e}^{S}\)), as described in Equation (19). \[\theta=\frac{A_{F}}{Sum_{e}A_{e}^{S}} \tag{19}\]  
We interpret the indicator \(\theta\) using Figure 4. The grey fields in the left side figure show the nominal area demand (\(A_{F}\)) for a square lattice-based occupancy grid in the case of traffic flows coming from the south and making a right turn at the intersection. In this example, \(A_{F}\) is equal to the sum of the areas of the elementary regions used to model the given turning traffic direction (\(Sum_{e}A_{e}^{S}\)), so the value of \(\theta\) is 1. Figure 4: Interpretation of the \(\theta\) indicator for different occupancy grids related to the right turning traffic direction. Figure 3: Illustrative example for the interpretation of indicator (\(\rho\)) used to evaluate the effectiveness of the discretization. The value of the indicator may of course differ from 1 if the elementary regions of the applied occupancy grid do not precisely overlap the area used according to the classical traffic engineering approaches. This is illustrated in the figure on the right, which still considers the right-turning traffic flow from the south. In this case, the nominal area demand is indicated by the blue area in the background, which is practically the same (and of the same size) as in the previous example. In yellow, we indicate the elementary regions of the hexagonal alternative occupancy grid that are used by the considered traffic flow. Using the dimensions of the elementary polygons described in the case of Figure 3, the value of \(\theta\) in this case is calculated to be 0.92. The closer the value of the indicator is to one, the better the conceptual grid covers the road surface along the conventional traffic engineering principles. However, if the value of the indicator is greater than one, the traffic flows can potentially be accommodated with a smaller area occupancy than the nominal area demand. The use of alternative grids provides the opportunity to model both priority traffic directions, infrequent, less typical vehicle movements, large vehicles, and emergency vehicles. Our aim in modelling emergency vehicles is to ensure priority. An occupancy grid that matches the intended route of the emergency vehicle ensures safe and efficient passage of the vehicle through the infrastructure element. In line with this, the area-dependent \(\rho\) indicator can help to select the occupancy grid that best fits the planned route. In this case, determining the movements (route) of the emergency vehicle is not part of the optimization task. The objective is to get the vehicle through the infrastructure element as quickly as possible. Therefore, it is appropriate to assume that the movement (and therefore the occupied route) of the emergency vehicle is a given constraint and to adapt the movement of the other vehicles to it during the optimization. For example, in a more complex junction modelled with a square occupancy grid, an alternative grid may be appropriate to implement diagonal vehicle movements. The alternative grid may even be designed from a different shaped and sized elementary region, such as a hexagon, where a greater number of connections between elements may result in a more efficient coordination of traffic flows. In this case, we can ensure the safety and reliability of traffic flows by defining the relationship between the original and alternative grids as described earlier in our concept.