In the Transport layer, there are two types of Internet Protocol are worked, namely- Transmission Control Protocol (TCP) and User datagram protocol (UDP). TCP provides connection oriented service and it can handle congestion control, flow control, and error detection whereas UDP does not provide any of service. TCP has several congestion control mechanisms such as TCP Reno, TCP Vegas, TCP New Reno, TCP Tahoe, etc. In this paper, we have focused on the behavior performance between TCP Reno and TCP Vegas, TCP New Reno over TCP Reno, when they share the same bottleneck link at the router. For instigating this situation, we used drop-tail and RED algorithm at the router and used NS-2 simulator for simulation. From the simulation results, we have observed that the performance of TCP Reno and TCP Vegas is different in two cases. In drop tail algorithm, TCP Reno achieves better Performance and throughput and act more an aggressive than Vegas. In Random Early Detection (RED) algorithm, both of congestion control mechanism provides better fair service when they coexist at the same link. TCP NewReno provides better performance than TCP Reno.