Markovich, Natalia M.Natalia M.MarkovichKrieger, Udo R.Udo R.Krieger2021-02-102021-02-102020978-3-030-66470-1978-3-030-66471-8https://fis.uni-bamberg.de/handle/uniba/49486The 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. We focus on the identification of the E2E delay and the longest per-hop delay distributions and the stochastic dependence of the associated random process. The E2E delay is determined by the sum of a random number of dependent per-hop (p-h) delays along the links of a considered overlay path and the longest per-hop delay by their maximum. We propose to use the sum of the p-h delays to get a distribution of the maximum which is motivated by the available statistical data of the E2E delays. 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. Using the extremal index we identify limit distributions of the maxima of the E2E delays and the maxima of the p-h delays at a path among all source-destination paths. Considering real-time applications with stringent E2E-delay constraints, 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 of a transport channel.engP2P networkEnd-to-end delayPer-hop delayTail indexExtremal indexQuality-of-servicePacket missing probabilityPlayback delayEquivalent capacityconferenceobject10.1007/978-3-030-66471-8_22