Two-criteria problem on hypergraphs for estimating data transmission quality on P2P networks

The relevance of this research is dictated by the fact that for video transmission modern networks have very high requirements for both building and maintaining a network infrastructure, and analyzing issues of uninterrupted delivery of content. The video stream is the basic type of streaming data in peer-to-peer networks. To improve the quality of streaming data services, various schemes for organizing the structure of a superimposed peer-to-peer network are used. Probabilistic statements of the problem that determine the quality of construction of a peer-to-peer network is known. For example, the probability of universal transmission, in which unpopular channels, along with popular channels, are also available for viewing by network users with a certain probability. In our work, a discrete two-criteria formulation of this problem for estimating data transmission quality is considered. Three finite sets are determined. The set of internet users, for example, viewers of internet television channels. The set of internet television channels and the set of streams into which streaming data can be distributed. Every internet user watches a channel and several streams are assigned to it for transmission. There are user-uploaded data streams into two types: a stream for own viewing corresponding to the television channel it is viewing, and a stream (one or several) of another television channel, exclusively for distribution to other users. A relationship of the following kind is constructed: the user watches some channel and distributes the streams for other channels. The theory of hypergraphs makes it possible to show in the systemic unity the ordered types of relations such as the edge of hypergraph. Each edge is assigned two indicators - weights, which mean such indicators of quality of service as coefficient loss of data packets and playback delay. Each edge constrains three vertices. Vertices of edge - users, channels and streams accordingly. The result of this assignment of flows to users should be to improve the level of performance of the broadcasting system, in particular, to reduce both the packet data rate loss and the playback delay. The mathematical model is described in the language of the theory of hypergraphs in a two criteria formulation. Two criteria have the type MINMAX, which allow simultaneously to take into account the efficiency indicators loss of data packets and playback delay. Copyright © 2018 for the individual papers by the papers’ authors.