No abstract

Background. Nowadays, file-sharing peer-to-peer (P2P) networks are becoming increasingly popular when providing video over the Internet. Successful reception of a given service is determined by how quickly and qualitatively the necessary content stored in the memory of the peers of this network is found. In structured systems a limited number of transitions are used to find the ordered file, however, for unstructured systems, where random search is used, the delay can be significant, especially when searching for rare files. At the same time, it is unstructured systems that can support complex requests with metainformation, which provides their priority development. There arises a question of how quickly the given file with a certain number of active peers can be obtained.Objective. The aim of the paper is the analysis of the state of downloaded content on the nodes of unstructured P2P networks.Methods. Synthesis of the mathematical model of video content replication taking into account the network load and performance analysis based on this model has been performed for the 3 most used algorithms: unified, proportional and "square root". Numerical quantitative studies have been performed by means of calculation.Results. A mathematical model that allows estimating the average number of attempts to replicate the ordered file taking into account the size of the network memory has been developed. The examples of the dependence of the average file search size for different numbers of active peers have been obtained.Conclusions. The mathematical model of video content replication necessary for the successful search of the requested file is obtained taking into account the network memory size determined by the number of active peers. The obtained dependence of the average number of request attempts when searching for the desired files for the three replication algorithms allows concluding that the "square root" algorithm is expedient.

Objective. The aim of the paper is the analysis of peer-to-peer network functioning quality in various load modes. Methods. A calculation of the selected quality index for various intensities of the occurrence of peers in the network based on the mathematical model of the network state and the solution of the integro-differential equation of dynamics is performed.Results. The analysis of the developed model has shown that in stationary operation conditions the quality as the relative value of upload and download speeds to the number of active peers in the network increases as the total amount of content offers increases. In conditions of non-stationarity, during periods of mass connection of new peers, the quality of the network may drop. Providers should encourage the altruistic strategy of peers.Conclusions. Analytical dependence of the peer-to-peer P2P network quality of broadcasting live streaming video on the components of this network has been obtained. Peer-to-peer P2P Internet networks provide a very popular service for the real time TV content delivery. Users of the P2P network in order to improve the quality of use should not immediately leave the network, which enables other peers to download the necessary fragments.