Dealing with the quality of the packet transport
of multimedia
services in
overlay networks, we present the relation between the missing probability $P_m$ of transmitted packets of
a variable bitrate
video stream and distributions
of the length
of the overlay path,
the upload capacity of nodes and
the playback delay at a destination node.
As
active streams
share the capacity of a transport channel,
we select
an equivalent bandwidth
based on a bufferless fluid-flow model.
A smallest equivalent capacity $u^*$ which provides the best
trade-off
between the mean delay between successfully delivered packets and the mean lossless time that is determined by the duration of
consecutive successful packet transmissions is proposed as an optimal upload capacity. $u^*$ is less than the peak rate. The playback delay $b$ is selected as a
quantile of a
packet delay distribution.
The normalized distribution of the length of the overlay path
is derived to be geometric.
The estimation of $u^*$ and $b$
requires inter-arrival
times between packets, packet lengths of a peer-to-peer video flow and
end-to-end packet delays.
For SopCast IPTV data it is concluded that the signaling traffic does not impact on %the value of
$u^*$ and increasing $b$
leads to the decrease of $P_m$.
