## 4 Network Model
### User Distribution Model
In this case, we will assume that \(q_{1}<q_{2}<\ldots<q_{n}\), where \(q_{n}\) is the length of the side of the maximum cell of the partition. Figure 7 shows the results of aggregation for the values \(q=1,14,56,255\) m\({}^{2}\), which corresponds to the values \(k=150,75,40,20,10\), respectively. To estimate the Hurst coefficient, we construct the dependence:  
\[lgd_{q}=f(lgq),q=1\ldots q_{max} \tag{7}\]  
Let us approximate dependence (3) by a straight line  
\[y(lgq)=algq+b \tag{8}\]  
For approximation, we use the least squares method, according to which:  
\[a=\frac{n\sum_{i=1}^{n}lgq_{i}lgd_{i}-\sum_{i=1}^{n}lgq_{i}\sum_{i=1}^{n}lgd_ {i}}{n\sum_{i=1}^{n}(lgq_{i})^{2}-(\sum_{i=1}^{n}lgq_{i})^{2}} \tag{9}\]  
Figure 4:0 Building aggregated structures. Figure 4:1  
The resulting dependence is shown in Figure 4:2  
Approximation obtained from the dependence of straight line and the estimate of the Hurst coefficient showed that for this structure \(H=0.7\), which corresponds to the fractal dimension \(D=1.3\). As mentioned above, the value \(d_{min}\) was introduced, which determines the minimum possible distance of the network nodes from the obstacle model. If the obstacle is assumed to be a certain structure, then the Hilbert curve may be viewed as a representative model of its extension (length) \(L\), and the mentioned value as its width (line width). Figure 4:3 Results of aggregation of the model structure at \(q=1\) m\({}^{2}\) (a), \(4\) m\({}^{2}\) (b), \(14\) m\({}^{2}\) (c) \(56\) m\({}^{2}\) (d). Then the total area of the simulated buildings \(S_{b}\) on the simulated territory can be determined as:  
Figure 4:4  
The share of the area occupied by buildings can also be considered as one of the structural parameters of the model:  
Figure 4:5  
where \(S=wh(m^{2})\) is the total area of the simulated territory, and \(w\) and \(h\) are length and width, respectively. Since \(d_{min}\) and the proportion of the area occupied by the buildings (obstacles) are linearly dependent on the length \(L\), which in this case is constant, then both \(d_{min}\) would have a similar effect on the properties of the modeled structure. In the example above, the area occupied by obstacles is 30%. To study the influence of this parameter on the properties of the structure, the dependence of the Hurst parameter on it was estimated. Figure 9 shows the dependence of the Hurst coefficient on \(d_{min}\). In this example, the range of change in \(d_{min}\) values is equivalent to the changes in the proportion of the obstacles area from 0 to 50%. From the results obtained, it can be deduced that the Hurst parameter increases with increasing \(d_{min}\), from 0.5 at \(d_{min}=0\), to more than 0.8 at \(d_{min}=5\) m (which corresponds to 50% of the area occupied by obstacles). A value of 0.5 is very reasonable, since when \(d_{min}=0\), there are actually no obstacles, and the location structure of the network nodes is a Poisson field (uniform distribution of nodes throughout the territory). With an increase in \(d_{min}\), the structure of the nodes' arrangement takes a form close to the fractal structure  
Figure 4:6 Dependence of the variance of aggregated structures on the size of the aggregation square. of the obstacle model, as can be seen from Figure 4:7 This structure has the properties of self-similarity, which is manifested in an increase in the Hurst parameter. With a further increase in \(d_{min}\), the area available for the placement of network nodes decreases so much that the example becomes irrelevant. Indeed, at close to 100%, all network nodes will be concentrated in one or more \"points\" (areas of a small area) of the service area. In addition, at a value of 100%, under the conditions of this problem, confusion occurs. This is attributed to the impossibility of placing network nodes in general. It is worth noting that these boundary conditions are only achievable theoretically, in practice, with \(\delta_{b}\) tending to 100%, the formulation of the problem itself needs an adjustment.