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We consider a "dynamic" model for a link jointly supporting two types of service: rate-adaptive and constant-bit rate services, e.g., ABR and CBR service in ATM networks. We construct and solve the associated two dimensional Markov chain via matrix-geometric techniques. This permits an analytical evaluation of performance when such services share resources. Moreover, when constant-bit rate connections are long lived relative to rate-adaptive connections (e.g., file transfers), we prove a separation of time scale result. This leads to a useful approximation that closely matches the performance in this regime.