The Generalized Stability Indicator of Fragment of the Network. II Critical Performance Event

The present paper is devoted to a detailed consideration of the criteria of criticality of the performance event. A complete classification of performance events will come to the formation of a probabilistic assessment of the generalized stability of the node-enterprise. This classification reflects the mutual influence of homogeneous nodes in the common corporate network.


Introduction
The set of all nodes (Fig. 1) in a common network somehow affecting the stability of the nodes [1][2][3][4][5][6], divided into four groups: direct vendors of ܲ , component group Н subnet with priority higher than the priority of the node ܲ , node group H subnet with a lower priority and a group of nodes with equal priority.
Probability space consists of all ordered N-lines, consisting of zeros and ones.

The conditions of a "critical performance elementary event"
We proceed to define the critical performance elementary event.Critical elementary event is the possible scenarios of work situations that arise due to the impact on the network nodes corporations force majeure, policy-exposure, or nodes suppliers [1][2][3][4][5][6].
Then the maximum amount ‫ܯ‬ ௦ of each type of resource ௦ that can be collected in a given time in favor of the affected node ܲ from all the nodes in a subnet H less than or equal priority, is . So, condition 3 of criticality of the elementary event is the following disjunction: Variable ξ ଵ ሺ௦ሻ ሺ‫ݐ‬ሻ denotes a random variable: the coefficient of performance of the contract of the j-th vendor.Condition 4. If only one force majeure situation has arisen in the subnet N of nodes ܾ ଵ , ܾ ଶ , . . ., ܾ భ , ‫ݎ‬ భ ାଵ , . . ., ‫ݎ‬ మ (nodes with greater or equal priority).
We denote the victim node via h, ݄ ∈ ൛ܾ ଵ , ܾ ଶ , . . ., ܾ భ , ‫ݎ‬ భ ାଵ , . . ., ‫ݎ‬ మ ൟ.Vector of demands ሺ‫ܣ‬ ଵ , ‫ܣ‬ ଶ , . . ., ‫ܣ‬ ሻ of the node as a result of force majeure has increased by a random value and become equal ሺηሺ‫ݐ‬ሻ‫ܣ‬ ଵ , ηሺ‫ݐ‬ሻ‫ܣ‬ ଶ , . . ., ηሺ‫ݐ‬ሻ‫ܣ‬ ሻ.This increased demands was directive distributed to the node ܲ and all nodes with priorities equal to or less than the priority of the node h.In this case, the node ܲ give away some fraction Δܸ ௦ of the total amount ܸ ௦ ‫ݏ(‬ ∈ ሼ1, . . ., ݉ሽ -type of resource) resources actually delivered to him in the considered period: Then condition 4 of criticality of the elementary event is the following disjunction: Therefore, we can assume that from node ܲ will be removed in favor of a node ݄ ଵ the following amount of resources Δܸ ; భ ௦ : after from node remaining resources will continue to be withdrawn to the node ݄ ଶ .The total number of remaining resources in the network after the elimination of force majeure in the node ݄ ଵ , which can be reallocated toward node ݄ ଶ : where Δܸ ; భ ௦ -amount already withdrawn from node ݄ resources in favor node ݄ ଵ : An additional amount of resources Δܸ మ ௦ necessary for the elimination of force majeure of the node . means that the node ܲ will be withdrawn to the node ݄ ଶ the next amount of resources Then condition 5 of criticality of the elementary event is the following disjunction: Force majeure occurred at two nodes ݄ ଵ , ݄ ଶ ∈ ൛ܾ ଵ , ܾ ଶ , . . ., ܾ భ , ‫ݎ‬ భ ାଵ , . . ., ‫ݎ‬ మ ൟ of subnet Н with equal priority.All required to restore the amount of resources is Combining accidentally increased demand nodes ݄ ଵ and ݄ ଶ actually results in the condition 5.
Condition 7. Force majeure occurred at two nodes of subnet H: ܲ and h with equal priorities.In this case we assume that other nodes in a subnet H help simultaneously to nodes ܲ and h.A critical situation arises if the total resources on the subnet H is not enough to help both of these two nodes.
The total additional amount of resources needed by both nodes is The maximum amount of resources that may be sent from nodes of subnet H towards affected nodes ܲ and h, is equal to Therefore, in this case, the condition is criticality if Condition 8.The last one.Force majeure occurred at two nodes ܲ and h of subnet H. Priority strictly greater than (priority ܲ ).

Conclusion
A simple analysis of options assures that these 8 conditions exhaust all possible cases of the distribution of zeros and ones in the N-line ሺε ଵ , ε ଶ , . . ., ε , δ , δ ଵ , . . ., δ య ሻ ; therefore, these conditions cover all possible elementary events.
In the following parts of the work are examples of the use of developed techniques of calculating the stability of nodes only in the places of interest of the chain map (for examples of regional structures and networks of homogeneous nodes companies), that is, in those places, which is the subject of our research.