A damped fixed-point approximation is proposed to characterize the throughput of persistent TCP and UDP flows in a network of router links supporting per-class queuing and Deficit Round Robin (DRR) scheduling among classes. In particular, we study the case of two classes where one of the classes uses drop-tail queue management and is intended for UDP traffic. The other class targeting TCP traffic is assumed to use Active Queue Management (AQM). The effectiveness of the proposed analysis method in this scenario is validated by extensive NS3 simulations. Moreover, we study, using the proposed fixed-point algorithm, the potential gain of employing the many-to-one communications paradigm with respect to the conventional one-to-one communications in which a client downloads a specific content from one server only.