## 4 Methods
### Connecting Alternative Networks-Through the Example of Large Vehicle Modelling
Accordingly, the predefined parameters of the model have to be adjusted as follows:  
* It is necessary to extend the _ORIG_ and _DEST_ matrices with the origin and destination locations of trucks defined on the alternative graphs (\(\textbf{ORIG}\in R^{(m_{p}+m_{h})\times(o_{O}+o_{A})}\) and \(\textbf{DEST}\in R^{(m_{p}+m_{h})\times(o_{O}+o_{A})}\) matrices);
* It is necessary to extend the \(D\) matrix with the shortest distances of the cells of the alternative graphs (\(\textbf{D}\in R^{(o_{O}+o_{A})\times(o_{O}+o_{A})}\) matrix);
* In addition to the size, shape, and position of the individual locations (cells), the possible directions of leaving the locations must be defined in the case of all representations. Transitions between the original and alternative representations cannot be allowed (passenger vehicles can only use the original, and trucks can only use the alternative graphs). For the proper handling of trucks and other large vehicles, the relationship between the created alternative graphs and the original graph must be specified. Equation (2) ensures that only one vehicle is present at a given location at a given time moment. It is necessary to extend the range of cases examined in the expression. Accordingly, all locations from the alternative graphs that overlap the examined location of the original representation must be taken into account in the expression, and vice versa. Let \(i_{AO}\) denote the locations of the alternative graphs that have a common spatial element (overlap) with the \(i_{O}\) location of the original representation, and \(i_{OA}\) the locations of the original representation that have a common spatial element (overlap) with the \(i_{A}\) location of the alternative graphs. Then, considering that one vehicle can be in a place at a time, and this must also be ensured in the case of overlapping model structures, the original Equation (2) should be replaced by the following two relations (Equations (16) and (17)). \[\sum_{k_{p}}x_{k_{p},j_{O}}+\sum_{k_{b},j_{AO}}x_{k_{b},j_{AO}}\leq 1\ ;\ \forall j,i_{O} \tag{16}\]  
\[\sum_{k_{p}j_{OA}}x_{k_{p},j_{OA}}+\sum_{k_{h}}x_{k_{b},j_{AO}}\leq 1\ ;\ \forall j,i_{A} \tag{17}\]  
For example, when examining the location \(i=5\) at a given time moment, the locations \(i=21\), \(i=25\) and \(i=40\) must also be included on the left side of the inequality. Accordingly, we must ensure that no more than one vehicle (regardless of whether it is a car or a truck) is present at locations 5, 21, 25, and 40 at a given time moment, since these cells have a common spatial element. Ensuring the connection between the graphs is also important to avoid collisions resulting from crossing vehicle movements (see Equation (4)). We also need to extend  
Figure 2: Road surface representation with a square grid-based structure extended by alternative cell structures—the angles and the gaps between the cells are only used for illustration purposes. the _R_CROSS_ matrix for specifying intersecting routes due to the increased number of considered locations (_R_CROSS_\(\in R^{(\omega_{0}+\rho_{A})^{2}\times(\omega_{0}+\rho_{A})^{2}}\)). In doing so, we must also pay special attention to the appropriate comparison of the routes marked in the original and alternative representations (routes with a common spatial element are also considered intersections in different graphs). In conclusion, if we want to coordinate the movement of small and large vehicles on the same occupancy grid whose elementary region is adapted to the size of the large vehicles, we are always forced to reserve a large region for the smaller vehicles. For many manoeuvres, it would be sufficient to reserve a smaller region. This is why it is so important that we have introduced the approach required to use alternative occupancy grids that can be applied simultaneously in an integrated manner. This approach could eventually lead to a reduction in resolution for smaller vehicles, which could affect accuracy in dense traffic scenarios or complex junctions.