Reliability Analysis of the Air Transportation Network when Blocking Nodes and/or Connections Based on the Methods of Percolation Theory

Abstract

The paper shows that to study the reliability and fault tolerance of air transportation networks, methods of percolation theory can be used, in which any aviation transport structure can be represented as a random non-planar, incompletely connected graph (nodes are airports, arcs are airlines). In the theory of percolation, one can consider the solution of the problems of finding the shares of blocked nodes and blocked connections for networks with various random and regular structures, in which they decompose into unconnected areas. The share of blocked nodes (in the node problem) or connections (in the connection problem), at which the conductivity between two arbitrarily selected network nodes disappears, is called the percolation (flow) threshold. For the same structure, the values of percolation thresholds for the bond problem and the node problem have different meanings. The percolation threshold value depends on the average number of connections per network node (density), and is a criterion for its reliability, i.e. determines the percentage of blocked nodes and/or communications that the network will lose the necessary level of performance ability. The dependence of the blocking threshold (percolation) on the network connection density can be expressed mathematically. Using a map of a real aviation transport network, it is possible to determine the average number of connections per one node and then calculate the threshold value of its predetermined reliability value. If the reliability threshold needs to be increased, then the necessary number of additional links can be calculated.