The Generalized Stability Indicator of Fragment of the Network. I. Modeling of the Corporate Network Fragments

In this paper we consider the stability of the enterprise-node that is functioning and has a network of homogeneous companies with regard to their interaction and influence on each other. This means that we come to consider the wider subnet model containing the node structure of homogeneous him nodes and their vendors. Consider also the parameters and factors that have a direct impact on the stability.


Modeling of the corporate network fragments in point of view of the generalized stability
In [1][2][3][4][5][6] defined stability of a single node based on its interaction with only vendors of various types of resources.It is one of the elements of the complex reference system enterprises [7,8].This means that we are in step (detail within the model ) and treated it only a small fragment of a node and its vendors.In fact, as a rule -is an abstract factor-node a subnet (in the algeb-Irina Nizovtseva raic sense of the term "factor"), i.e. the union of the whole structure of their own kind one-profile units that are represented on the diagram as a single unit.
Subnet homogeneous nodes Н is a component of the homomorphism kernel → ା acting in the formation of the next, more general model.This subnet of homogeneous nodes under the influence of the homomorphism H moves (combined) in the model into a single abstract node [5].

Fig. 1. Fragment of a network diagram
Let us turn to the more complex and detailed case where we are interested in the node-enterprise functions in a corporation network and itself is part of a subnet of their own kind nodes.A fragment of a network diagram is shown in Fig. 1.
For the generalized coefficient of stability of network fragment ሼ‫,ܣ‬ ܲ , ‫,ܤ‬ ‫,ܥ‬ ‫,ܦ‬ ‫,ܧ‬ ‫ܨ‬ሽ in Figure 1 can be taken stability coefficient of the node Р 0 in a more general abstract network.More precisely, the generalized stability of the subnet Н of the network G(N,A) be called the stability of the node ݄ ൌ φሺ‫ܪ‬ሻ -the image of a subnet Н under the natural homomorphism φ: ‫ܩ‬ → ‫ܩ‬ ‫ܪ‬ ൗ on the factor-network ‫ܩ‬ ‫ܪ‬ ൗ (Fig. 2).
Graphical interpretation of the generalized stability The generalized stability factor shows how reliable and stable operating analyzed fragment of the whole network, the entire network fragment is regarded as a node.
Thus, the concept of external stability of the node and its internal stability from a formal point of view, are one and the same concept (the same numerical characteristic with the same method of calculation) applied at different steps of the considered morphisms chain network structures

Factors
Let's keep in mind that we are interested in the node ܲ -this is, for example, the structural unit of a larger structure Н of homogeneous nodes.
Statistical certain stability coefficients of all nodes of suppliers for all the nodes that make up the subnet investigated Н.
2. Each node ݄ substructure Н comprising nodes uniform profile that requires a supply of the same species consumed products ‫ܣ‬ ଵ , ‫ܣ‬ ଶ , . . ., ‫ܣ‬ , wherein ‫ܣ‬ a denotes the volume of the desired product supply node k-th species.
3. Influencing factor on the subnet Н external environmental conditions and different force majeure (accidents, natural disasters, etc.).Let the requirement of individual node (fig.3) subnet Н a result of accidents increases with the random variable [6] ηሺ‫ݐ‬ሻ is proportional to the ܸ -standard average needs, so ܸሺ‫ݐ‬ሻ ൌ ηሺ‫ݐ‬ሻ ⋅ ܸ .4. An essential feature of the proposed model and the new element becomes the accounting impact of foreign policy on the subnet from a superior organizational and regulatory authority.This can be forced redistribution of resources within the subnet Н in case of force majeure situation on one (or even several) of its nodes.In addition, the regulatory impact on an individual node or group of nodes subnet Н can be exercised for any other reason (economical or technical).Redistribution is not an arbitrary manner, but with the priority of the normal functioning of a particular node, given its importance for the overall production process.Also take into account the amount of expenses for redistribution.Each node subnet N is associated with a natural number -the priority of the node.
The set of all nodes in a common network somehow affecting the stability of the site, divided into four groups: direct vendors of ܲ , component group Н subnet with priority higher than the priority of the node , node group N subnet with a lower priority and a group of nodes with equal priority (Fig. 4).  1 and 2).
Coefficients ‫‬ ଵ ೖ ሺሻ assumed to be defined on the basis of observations and statistical studies; amount of supplies to enter into treaties (the third row of the  2. Homogenies nodes of subnet Н

Conclusion
So, developed methods for determining and calculating the stability of the host (as the network characteristics) are so universal and applicable (with the necessary potential interpretive) anywhere on the network under consideration of

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the chain of mathematical models of the structures of corporations from any industry.
The next part will be detailed formalized critical performance situations.The formalization will develop a methodology for calculating the generalized stability of the enterprise.

Table 1 .
table) for each desired product is exactly equal to the demands ‫ܣ‬ .Vendors of node 0