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Transmission control protocol (TCP) provides reliable end-to-end communications between any two devices on the Internet. Slow start mechanism is used when a source machine starts sending data to a destination, or when a TCP connection suffers packet loss and a retransmission timeout has occurred. Congestion avoidance mechanism is then used to transmit information with sustainable data rate from the sender to destination. In this paper, novel designs of the Slow-Start and congestion avoidance mechanisms will be discussed. The Slow Start threshold parameter is removed to create a simple and responsive design. Based on TCP Vegas, a new congestion avoidance design with two reduction rates on a connectionpsilas congestion window parameter is introduced. A smoothing average of the round-trip propagation delay is estimated. Simulation results indicate that the proposed designs fairly share network resources among TCP connections, and operate harmoniously with TCP NewReno connections in networks. The designs of both the slow-start and congestion avoidance processes are simple, and require no modifications to TCP protocol specification.