We consider the dimensioning problem for Internet access links carrying TCP traffic with two priority classes. To this end, we study the behaviour of TCP at the flow level described by a multiple-server Processor Sharing (PS) queueing model with two customer classes, where the customers represent flows generated by downloading Internet objects; the sojourn times represent the object transfer times. We present closed-form expressions for the mean sojourn times for high-priority customers and approximate expressions for the mean sojourn times of low-priority customers. The accuracy of the model is demonstrated by comparing results based on the PS model with "real" TCP simulation results obtained by the well-known Network Simulator. The experimental results demonstrate that the model-based results are highly accurate when the mean object size is at least 10 IP-packets, and the loss rate is negligible