Statistical Analysis of the End-to-End Delay of Packet Transfers in a Peer-to-Peer Network

The paper is devoted to the statistical analysis of the end-to-end (E2E) delay of packet transfers between source and destination nodes in a peer-to-peer (P2P) overlay network. The E2E delay is determined by the sum of a random number of per-hop (p-h) delays along the links of a considered overlay path. We propose to use the maximum of the p-h delays instead of the sum. Based on recent analytic results derived from extreme-value theory we show that such sums and maxima corresponding to different paths may have the same tail and extremal indexes. These indexes determine the heaviness of the distribution tail and the dependence of extremes, respectively. Using the extremal index we identify limit distributions of the maxima of the E2E delays and the maxima of p-h delays at a path among all source-destination paths. The distributions are used to identify quality-of-service (QoS) metrics of a P2P model like the packet missing probability and the corresponding playback delay as well as the equivalent capacity.