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An approximate analytical formulation of the packet level and link layer qualities of service (QoS) for variable bit rate multiclass services in a cellular random carrier-hopping multirate multi-carrier (MC) DS-CDMA system is presented. The novelty of this paper is that the packet buffers for each subcarrier at the mobiles in the uplink of this system are viewed and modeled as leaky buckets. A leaky bucket is a policing device commonly used to regulate and enforce traffic agreements. The relationship for the packet loss probability in a subcarrier in terms of its outage probability in the subcarrier, and the relationship for the outage probability in the subcarrier in terms of the number of connections, the mean subcarrier on/off periods and packet level QoS metrics, like the mean packet buffering delay in each subcarrier, are explicitly derived. Numerical results illustrate that the packet loss probability and outage probability in an MC-DS-CDMA subcarrier channel can be lowered by having a smaller number of subcarriers.