Research of complete homogeneous "greedy-vertices" resource networks: zone of "sufficient large" resource

Resource network with greedy vertices – the modification of the graph dynamic model "resource network". At each discrete-time moment the graph vertices transfer resources to each other through the edges with limited throughput, first passing the available resource to themselves via the loop and then distributing the remaining resource (if it is available) to outgoing edges according to the "standard" resource network rules. These are two rules with threshold switching: if the vertex has resource, that exceeds the total throughput of all vertex's outgoing edges, it transfers the full throughput to each outgoing edge; otherwise, it gives away the entire available resource, distributing it in proportion to the throughputs of the outgoing edges. The particular case of a complete homogeneous resource network with "greedy" vertices is considered. For networks of such type there are two total resource thresholds, separating zones of different network behaviour: the first threshold divides the zones of "insufficient" and "sufficient" resources, the second divides the zones of "sufficient small" and "sufficient large" resources. In the article the last zone – "sufficient large" resource – is investigated: the functioning of the network is described, the asymptotic state is found.