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In spite of the larger performance gain such as higher throughput and almost zero packet retransmissions compared to TCP Reno, TCP Vegas still has a few obstacles for it to be deployed in the Internet. Studies have shown unfair treatment to Vegas connections when they compete with Reno connections. Other issues identified with TCP Vegas are problems of rerouting, persistent congestion, and discrepancy in flow rate tied with starting times and link bandwidth. We reinvestigate these issues rind propose modifications to the congestion avoidance mechanism of the TCP Vegas, with the slow-start and congestion recovery algorithms of Vegas remaining untouched. Unlike the solutions proposed in the recent past to deal with some of these issues, our solution it neither dependent on any critical parameter values nor on the buffer management scheme at the routers (e.g., RED). Our experiments show that the modified TCP Vegas (Vegas-A) it able to obtain a fairer share of the network bandwidth when competing with other TCP flows. We also show that Vegas-A can tackle rerouting issues and rectify Vegas's bias against higher bandwidth flows. At the same time, our experiments prove that Vegas-A preserves the properties of Vegas that have made it a noteworthy protocol.