# Analytical Model for Information Flow Management in Intelligent Transport Systems
## 3 Theoretical Studies
The drawback of the proposed method consists in the fact that the capacity of a system's object can be determined based solely on empirical data. This drawback can be eliminated with the use of analytical methods for obtaining the values forming the Pareto set, i.e., the multicriterion problem methods where sets of possible environment states are classified according to the principle of the hierarchical relationship between the probabilities of their occurrence (zoning methods). The main principles of the zoning method rely on hierarchical relationships between the probabilities of possible environmental states (ESs) and are as follows:  
1. Since zoning represents an inverse parametric problem of linear programming, it is expedient that zoning is performed based on the principle of maintaining a preset hierarchical relationship between all possible environmental states, not according to the dominant effect principle. 2. When dealing with \"game with nature\"-related problems, it is expedient to use vector optimization techniques, and many multicriterion problems can generally be solved using the tools of game theory of nature. When passing from a multicriterion problem to a \"game with nature\", the probabilities of nature states \(p_{j}\) are coincident with relative significance coefficients for criteria \(\mathrm{c}_{j}\), i.e., \(p_{j}\equiv\mathrm{c}_{j}\). 3. The procedure for zoning that uses hierarchical relationships between the probabilities of possible environment states is determined by manifestations of the ESs under analysis. Let us form an effectiveness matrix of possible actions under various environmental states. Any task relating to decision-making optimization is characterized by three basic concepts--a set of candidate decisions; a set of environmental state types; and the efficiency of a proposed decision under each environment state. Here and elsewhere, we shall use the following designations:  
* \(m\)--number of possible action scenarios;
* \(n\)--number of possible environmental states or criteria that correspond to them;
* \(a_{ij}\)--effectiveness of \(i\)-th action for \(j\)-th criterion, \(i=\overline{1,m}\), \(j=\overline{1,n}\). Then, the effectiveness matrix of action scenarios under various ESs shall have the form:  
\[||a_{ij}||= \begin{pmatrix}a_{11}&a_{12}&\ldots&a_{1n}\\ a_{21}&a_{22}&\ldots&a_{2n}\\ \ldots&\ldots&\ldots&\ldots\\ a_{m1}&a_{m2}&\ldots&a_{mn}\end{pmatrix}  \tag{11}\]  
It has been found in studies [21; 41; 42; 43; 44] that there is a relationship between the Pareto set in multicriterion tasks and the zoning method for solving \"games with nature\"-related problems under uncertainty [45; 46; 47; 48]. Provided that the effectiveness function of the differential state vector is continuous, the matrix game with nature can be reduced to a linear vector optimization problem [49; 50; 51; 52]. The distribution of the effectiveness relative significance coefficients is constrained by  
\[0\leq\mathrm{c}_{j}\leq 1,\;j=\overline{1,n},\;\sum_{j=1}^{n}\mathrm{c}_{j}=1, \tag{12}\]  
i.e., it is determined by a set (\(n-1\)) of independent values. Every possible complete set of ES distributions corresponds to a distribution field presented as a rectangular hypertetrahedron in dimensional space (\(m-1\)) [53; 54; 21; 55]. In the Cartesian coordinate system \((\mathrm{c}_{1},\mathrm{c}_{2}\ldots,\mathrm{c}_{n-1})\), this hypertetrahedron is a product of the intersection of a positive hyperoctant by a hyperplane that cuts on each coordinate axis a segment equal to unity [56; 57; 58; 59; 60].