## 4 Network Model
### Environment Model  
Let us begin with an introduction of the environment model in which, when constructing a network model, we can start from the conditions of urban infrastructure, considering that elements such as walls of  
Figure 1: Users’ distribution in the service area. buildings and other structures are obstacles to the propagation of radio signals. These elements incorporate external attenuation, the sum of which might be significant. We will also assume that the considered elements of the access network (subscribers of the mobile communication network, the Internet of things) are located at arbitrary points and are outside these elements. It is easy to see that the key elements of the image on the maps of settlements are a rectangle or line segments connected at right angles. It is also easy to notice that when you change the scale, i.e., enlargement of the object, a building, a quarter, a micro-district, in general, its shape is almost preserved. This allows us to conclude that these structures are self-similar, which is typical for elements of fractal geometry. The problem of numerically describing natural and artificial forms is well known, for example, as the \"coastline paradox\" [23]. In particular, the issue posed is that an increase in the accuracy of measuring the length of the coastline contributes to an increase in its numerical estimation. Thus, the length does not give the object a sufficiently complete characterization, especially when it is necessary to compare the objects. This problem has led to the emergence of such a characteristic as a fractal dimension. For example, as shown in the literature [24; 25], we can talk about comparing the shape of the coastline of Norway and Great Britain. The fractal dimensions of Hausdorff are 1.52 and 1.30, respectively. Figure 2 shows fragments of the coastlines of Norway and Great Britain according to data from the Google Earth system [26]. As you can see from the above figures, these lines differ significantly. In particular, it is recognized that the coastline of Norway is the longest in Europe. This can be clearly seen from the above fragments, the shape of the coastline of Norway is varying more from a straight line than the shape of the coastline of Great Britain. Estimates of the fractal dimension describe these variations numerically. The user distribution model in the service area should be associated with the environment model, such as buildings and other structures in the urban structure or to other natural features of the terrain (hills, mountains, water bodies, etc.). For this purpose, let us first consider a model of the user's environment in a typical urban structure. Figure 2: Fragments of the coastline of Norway (**a**) and Great Britain (**b**). Similar to the case of coastline, the user environment in an urban structure is an obstacle to both user placement (walls of buildings and structures) and signal propagation. These obstacles form a kind of geometric figure whose boundary outline, like the outline of the coastline, determines the characteristics of the given environment. Considering this analogy, it is very common to extend the idea of the fractal dimension to the definition of the properties of the system. In this work, we propose to use geometric fractals in the problem of modeling the network structure. In particular, if the elements of the described structure are mainly flat rectangular elements, structures such as the Peano curves or the Sierpinski carpet [27; 28] can be considered, as shown in Figure 3.  
Figure 4a depicts a fragment of a city map image (St. Petersburg, Russia), in which buildings and open areas (courtyards, sidewalks, carriageways) are highlighted. Figure 4b shows the fragment of the Hilbert curve [25]. In modeling, we will assume that the curve line simulates an obstacle. The line does not have a width. However, when selecting the location of the mesh elements, a conditional minimum distance between the mesh element and the points of the curve (minimum distance) \(d_{min}\) can be entered.