Dynamic hypergraphs of renewal processes in mobile networks.

Abstract

The characteristics of random geometric hypergraphs are studied as mathematical models of scalable wireless computer networks. An efficient algorithm for finding cliques in geometric graphs, constructing hypergraphs from geometric configurations has been developed. The types of hyper-edges in hypergraphs generated by a scalable configuration have been identified. The influence of random failures of nodes of computer networks and their restorations on the dynamics of hypergraphs of networks is considered. The analysis of the dynamics of the number of active nodes depending on the type of probability distributions of uptime and recovery time is carried out. The dependences of the mathematical expectation of the number of hyper-edges of certain types in the geometric hypergraph of a wireless computer network on the network operation time, on the radii of zones of reliable reception / transmission of a signal, on the ratio of the parameters of local recovery processes are obtained. The presentation of the results is accompanied by charts.