Differentiated Service networks (DS) are fair in the way that different types of traffic can be associated to different network services, and so to different quality levels. However, fairness among flows sharing the same service may not be provided. Our goal is to study fairness between multirate multimedia sessions for an assured DS service, in a multicast network environment. To achieve this goal, we present a fairness mechanism called Session- Aware Popularity Resource Allocation (SAPRA), which allocates resources to multirate sessions based upon their number of receivers. Simulation results in a multirate and multi-receiver scenario show that SAPRA maximizes the utilization of bandwidth and maximizes the number of receivers with high-quality reception.