## 3 Results: The Theoretical Geometrical Model and Its Application for Budapest
### Application of the Geometrical Model: Results for Budapest  
After developing the graph theory-based notation of the geometric model, we are going to present it in a numerical example as well. The object of the numerical example is the previously examined network from Budapest. This is a good example of the real geometrical model, as the central ring and the rays can be clearly defined, but it is distorted at the same time--there are several branches in it, and one of the central CSDLs is not exactly fitting to the central ring (SM013). It should be mentioned that in the case of three pairs of shopping malls, the distance between them is close to zero, so they could even be served together with a common cross-dock in a new system. The examined geometrical model with the graph-theory-based notation can be seen in Figure 14. To the polygon of the central ring, an ellipse can be fitted instead of a circle, its major axis is 4.7 km, and its minor one is 3.5 km. On the figure, at the branches *, **, and *** are used to show those rays which belong to the same central CSDL.  
For the examination of the geometrical model of the shopping malls in Budapest, all the main indicators were calculated (distances, goods amount, number of CSDLs) and were defined and described in the previous sections. The results can be seen in Table 2.  
Figure 13: Geometrical model of a real city logistics system of the concentrated sets of delivery locations with slashes and then simplified, in the case of \(n=6\).  
The examined geometrical model is far from a symmetrical structure; additionally to the branches, the length of the rays, the number of CSDLs, and the estimated amount of goods are fluctuating. It was also examined whether any correlation could be detected between the length of the rays, the number of CSDLs on them, and the estimated average amount of goods, but the analysis showed no correlation; presumably, much more traffic characteristics, the size of the CSDLs, and the degree of concentration may be related to the quantities of goods.  
Thus, we developed the theoretical, the reference, and the real geometric model of the city logistics system of the CSDLs and its notation based on graph theory, which was also applied to the examined Budapest example. Earlier, it was concluded, based on the simulation results using the specified geometrical model, that the cargo bike-based city logistics concept can be a right development direction because by integrating a relatively small number of cargo bikes into the system, many stores could be served. Additionally, a significant share of all freight demand in such a system could be served by using the bike path network instead of the already congested urban road network. By developing this complex model, and its exact notation, it became possible to examine the similar city logistics system in an exact way, and it became possible to examine that reference geometrical model in the future, which can later function as a benchmark in similar developments. Naturally, there are several further questions in this research which we would like to present next.