Many resource allocation schemes have been proposed based on different criteria such as system throughput, fairness, transmission power, user priority and others. According to the 3GPP specifications, however, as long as a GBR (guaranteed bit rate) bearer is admitted, eNB has to allocate resource blocks (RBs) for this bearer to ensure its transmission right. At the same time, eNB also must distribute the remaining RBs to non-GBR bearers so as to achieve high radio resource utilization. However, 3GPP has not specified how to measure GBR. In this paper, we use exponentially weighted moving average (EWMA) to define the measurement of data rate and show that it is beneficial to the scheduling on both UE and eNB sides. We also present a scheduling scheme, AAG-2, which aims at ensuring QoS for all inprogress GBR sessions, while at the same time efficiently allocating RBs to non-GBR sessions.