  We study in this paper the integration of elastic and streaming traffic on a
same link in an IP network. We are specifically interested in the computation
of the mean bit rate obtained by a data transfer. For this purpose, we consider
that the bit rate offered by streaming traffic is low, of the order of
magnitude of a small parameter \eps \ll 1 and related to an auxiliary
stationary Markovian process (X(t)). Under the assumption that data transfers
are exponentially distributed, arrive according to a Poisson process, and share
the available bandwidth according to the ideal processor sharing discipline, we
derive the mean bit rate of a data transfer as a power series expansion in
\eps. Since the system can be described by means of an M/M/1 queue with a
time-varying server rate, which depends upon the parameter \eps and process
(X(t)), the key issue is to compute an expansion of the area swept under the
occupation process of this queue in a busy period. We obtain closed formulas
for the power series expansion in \eps of the mean bit rate, which allow us to
verify the validity of the so-called reduced service rate at the first order.
The second order term yields more insight into the negative impact of the
variability of streaming flows.
