The paper contributes to the teletraffic analysis and quality of service of packet
transmission of peer-to-peer systems. We look at the packet transmission processes that are
induced by a peer-to-peer overlay disseminating real-time traffic from a statistical perspective.
Applying the theory of extreme events, we derive that the asymptotic distribution of the
end-to-end packet delay (i.e. packet delivery time between sender and receiver peers) is
subexponential heavy-tailed if the inter-arrival times between packets are regularly varying
heavy-tailed distributed. To evaluate the probability to miss a packet as a quality-of-service
attribute one requires a set of observable variables based on the realized flows such as the endto-
end packet delays, the packet inter-arrival times and packet lengths of single or aggregated
streams associated with a peer.
