—Traffic modeling is key to the capacity planning of data networks. Usual models rely on the implicit assumption that each user generates data flows in series, one after the other, the ongoing flows sharing equitably the considered backhaul link. We relax this assumption and consider the more realistic case where users may generate several data flows in parallel, these flows having to share the user's access line as well. We derive explicit user-level performance metrics like mean throughput and congestion rate in this context, assuming balanced fair sharing between ongoing flows. These results generalize existing ones in that both match in the limit of an infinite number of access lines.