## 4 Methods
### Connecting Alternative Networks-Through the Example of Large Vehicle Modelling  
In the developed model, the unit regions of the lattice representing the road network were sized for passenger vehicles. In order to handle larger vehicles in the model, there are two basic ways:  
* the vehicles are still treated as a unit, therefore cell size has to be increased, or
* the cell size remains the same, then a larger vehicle occupies more cells at a given time. In our case, the first method seems more reasonable, considering the constraints describing the model (e.g., the system of equations determining that a vehicle can only be in one location at a time). Furthermore, this method supports more realistic modelling: the central system defines the trajectories of the vehicles; however, the realization of real vehicle movements within the cells relies on the vehicle's sensors. In the case of the second method (a vehicle can occupy several cells simultaneously), a more precise definition of vehicle movements would be necessary, which can be a particularly difficult task in the case of large vehicles without pivot joints. To ensure that the efficiency of the basic model does not decrease due to the use of a larger cell size, we propose to create one (or more) alternative representation(s) of the same road network. Following this approach, several structures can be created consisting of different-sized and shaped regions for different vehicle categories and special traffic directions. Following this:  
* normal size vehicles are handled on the original graph (lattice);
* trucks are moved along the same principles, but on an alternative graph(s) with a larger cell size structure;
* the relationship between the original and alternative graphs is to be defined. To exclude collisions, no more than one vehicle may be present at a spatial point at the same time, regardless of the type of vehicle. Based on this approach, it is necessary to model the road network using larger size cells considering:  
* the characteristics of the developed model: the values of speed, acceleration, and deceleration are derived from the size of the cells travelled during the time units, so larger cell sizes could result in high speeds of the trucks;
* aspects of efficient traffic management: large vehicles traveling on larger cells occupy a large spatial area during the time steps (moving from one cell to another), while during each time step, a part of the large cells is free (and could even be passed through by smaller vehicles). We can effectively implement the above-mentioned aspects by using overlapping cells in the case of alternative graphs (e.g., for describing the movements of trucks or large vehicles). Overlapping cells allow the speed to be adjusted realistically and make the system more efficient. In the case illustrated in Figure 2, for example, the size of the cells of the alternative lattice structures (middle and right-side figures) is twice the size of the original cells, which were shifted with the original cell sizes. Several alternative representations of the same road network (with sufficiently large cells) can be used to manage different vehicle categories, emergency vehicles, and special traffic directions. As Figure 2 illustrates, the efficiency can be improved even further in this way, since it is not necessary to increase the lateral size of the cells for a realistic description of the traffic movements. For example, the truck moving from location \(i=17\) to \(i=34\) covers route (17-21-25-43-30-34). The alternative graphs increase the number of considered locations (\(o\)). In the following, the total number of locations of the original representation is denoted by \(o_{O}\), while the number of all locations of the alternative mappings is denoted by \(o_{A}\). The number of considered passenger cars is denoted by \(m_{p}\), and the number of trucks by \(m_{h}\).