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This paper proposes a fair, rate-based end-to-end congestion control mechanism for multimedia traffic in packet switched networks such as the Internet. The scheme is modeled after a non-linear system. The congestion is controlled by adjusting the transmission rates of the sources in response to the feedback information from destination such as the buffer occupancy, packet arrival rate and service rate, so that a desired quality of service (QoS) can be met. The QoS is defined in terms of packet loss ratio, transmission delay, power and fairness. The performance and stability of the system is analyzed mathematically. The proposed scheme has been implemented in the NS-2 simulator. Simulation results demonstrate the performance of the scheme to be in agreement with mathematical analysis. The proposed scheme is shown to provide considerable improvements in terms of the QoS metrics over New-Reno TCP technique.