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In DiffServ-aware traffic engineering, a key issue is how to properly allocate bandwidth for different DiffServ class types. Recently, a cumulative allocation strategy, called the Russian doll model (RDM), has gained intensive interests in IETF. The basic RDM, however, only describes the necessary condition of a stable queuing system: the utilization factor must be less than unit. When applied to the real world, the RDM must take the measures of QoS into account. In this paper, we establish a QoS-aware RDM on the fractional Brownian motion process model.