Integration of streaming services and TCP data transmission in the Internet

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 ε≪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 ε. 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 ε 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 ε 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.