Modern multi-service networks are inseparably linked with the commercial concept "triple play" that implies simultaneous provisioning of telephony, television (broadcast television and video on demand) and data transmission (mostly TCP-based best effort traffic) over a single broadband connection. These services generate traffics of three types - unicast streaming, multicast streaming and elastic traffics. In this paper, we propose and analyze a multi-service model of a triple play single-link network. Many research teams, including authors of the present paper, were not able to find any exact analytical solution or recurrent algorithm for models with a mixture of streaming and elastic traffics. We succeeded in developing and evaluating an approximation valid for the calculation of the elastic traffic mean transfer time for the proposed realistic traffic model. © Springer-Verlag Berlin Heidelberg 2011.