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Exploitation of the statistical multiplexing gain in the delivery of compressed videos is essential for achieving efficient network resource utilization. This paper proposes an analytical framework based on a GOP-aware effective envelope for guaranteeing statistical quality-of-service (QoS) to an aggregate flow from a class of connections. The GOP-aware effective envelope intends to model more realistic traffic burst by taking the information of individual flow's launch time and group-of-picture (GOP) into account With this information, the QoS guarantee is applicable not only to the aggregate flow but also to individual flows. Through numerical experiments, we show that the significant improvement on multiplexing gain can be achieved, particularly, under those cases with short delay bounds and small-to-moderate aggregation scales.