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An analytical formulation of the outage probability in terms of bit error rate specification for variable bit rate (VBR) multiclass services in the uplink of a dynamic complete group partitioning (DCGP) round-robin carrier-hopping multirate multi-carrier (MC) DS-CDMA cellular system is presented. The analytical framework is formulated for the general case in which different traffic classes have different spreading gains in each of the subcarriers. The analytical work leads to the determination of the capacity region of this system for VBR traffic. Numerical results show that the system capacity with DCGP can be larger than those with complete sharing (CS) and dynamic complete partitioning (DCP) of the subcarriers.