Conservative nature of Vegas creates less opportunity to get fair share of bandwidth then Reno in wired network. On the other hand, aggressive nature of Reno helps to achieve more share of bandwidth. Both Reno and Vegas assumes that congestion occurs in the forward rather than in reverse path. In asymmetric network the path characteristics of forward and backward is different.In this work, we propose a network model and analyzed the Inter-protocol fairness between TCP Reno and TCP Vegas with some queue management techniques such as Droptail and random early detection (RED) in asymmetric network where the forward and backward path has different characteristics. The simulation experiment results using NS2 indicates that use of RED can achieve better fairness than Droptail in asymmetric network.