Another version of TCP called TCP Vegas has been proposed and studied in the literature. It can achieve better performance than the current TCP Reno. In our previous studies, steady-state behavior of a windowbased flow control mechanism based on TCP Vegas has been analyzed for a simple network topology. In this paper, we extend our analysis to a generic network topology where multiple bottleneck links exist. We first derive equi- librium values of a window size of a TCP connection and the number of packets waiting in a router's buffer in steady state. We also derive throughput of each TCP connection in steady state, and investigate the effect of control parameters of TCP Vegas on fairness among TCP connections. We then present several numerical examples, showing how control parameters of TCP Vegas should be configured for achieving both stability and better transient performance.