Computational Mathematics and Mathematical Geophysics in honor of academician Anatoly Alekseev's 90th Birthday

8-10 October, Novosibirsk

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Rodionov A.  

Arithmetical mean of mathematical expectations of maximum flows between pairs of nodes as index of a network's troughput

The task of obtaining an arithmetic mean of mathematical expectation of a maximum flow between all pairs of nodes in a random network with unreliable links is discussed. We use random graph G as a model of such network. This index shows throughput of a modelled network in a whole. The task of obtaining a mathematical expectation of a maximum flow between a specific pair of nodes in a random graph is not new. It is obvious that exhaustive search of mathematical expectations of a maximum flow for all pairs of nodes is ineffective, as all possible states of G must be examined for each pair. When reversing the task to considering all maximum flows for each state, a number of operations decreased significantly, but multiple repeated calculations still take place. In the current paper some special methods for speeding up the process are proposed, which allow re-usage of some intermediate results in calculation of maximum flows between several pairs of nodes.