## 3 Task Statement  
In this section, the task statement is described, where each individual case may be unique when building a mobile communication network, and in any case, a decision about the choice of the locations of the base stations is made. However, in networking scenarios, many similarities can be found. Obviously, there is something in common for building networks inside the city, outside the city, along highways, indoors, etc. The generality of these cases is dictated by the density of users and the structure of the environment. Having a summary of the distribution of users and the characteristics of the system, it is thus possible to describe those cases and to identify their features and characteristics. We should obviously determine where we want to create a network: outdoors or indoors. It should be noted that, in this case, the distinction between the network outside or inside the premises is important, but not essential, since it is determined based on the characteristics of the user's environment. These features are different for an indoor or outdoor network. Therefore, without compromising generality, one of these alternatives may be chosen. We would also accept the first alternative, i.e., the outdoor network. Let us assume that users are evenly distributed over the territory where they can be located, i.e., on the territory outside the building elements (buildings and other structures). Uniform distribution of users on the plane occurs where the coordinates along the abscissa and coordinate axes are arbitrary, independent, and distributed according to a uniform distribution. Such a distribution is also referred to as the Poisson field or Poisson point process [21]. The probability that \(k\) points (users) \(p_{k}(S)\) will fall to any region \(s\) is defined only by the area of that region and is calculated by the Poisson formula:  
\[p_{k}(S)=\frac{(\rho S)^{k}}{k!}e^{-\rho S} \tag{1}\]  
where \(\rho\) is the number of users per unit area (density), \(S\) is the area of the region. However, if there are structures in the service area, which are also generally randomly distributed, this probability becomes dependent on the chosen coordinates. In general, it can be described by the conditional probability  
\[p_{k}(S)=\frac{(\rho A)^{k}}{k!}e^{-\rho A},A=S(s)-S(s\cap b_{i}),i=1,\ldots,n \tag{2}\]  
where \(b_{i}\) is the area occupied by the \(i\)-th building, \(n\) is the number of buildings. Figure 1 shows an illustration of this distribution. The highlighted area \(s_{1}\) corresponds to the first case \(s\cap b_{i}=\phi,i=1,\ldots,n\), the second area \(s_{2}\) to the case \(s\cap b_{i}\), the third area \(s_{3}\) to the case \(A=S-S(s\cap b_{i})\
eq\phi\). It can be shown that if \(b_{i}\) are random and independent, then the resulting distribution of users is a Markov Modulated Poisson Process (MMPP) [22]. However, if the properties of the environment described by \(b_{i}\) differ from those indicated, the resulting process will have different properties. This is quite expected, as the distribution of users across the territory under consideration, taking into account its structure, is increasingly unequal. Moreover, the properties of this distribution depend on the properties of urban development. For any particular instance, the features of the environment are different. However, the degree of variation between one structure of the environment and another will not be important. In this context, in order to build a mobile network, it might be useful to be able to describe the environment in a certain manner, which would facilitate the comparison of different territories and the choice of typical solutions. Therefore, in order to describe the properties of the distribution of users across the service area, it is necessary, under the assumptions made, to describe the characteristics of the distribution of buildings and structures.