Motivated by the deployment of wide-area high-speed networks, we propose GENEVA, the streaming control algorithm using generalized multiplicative-increase/additive-decrease (GMIAD). Because current typical congestion controllers such as a TCP-friendly rate control prevent occurrences of network congestion reacting susceptibly to packet loss, it causes a significant degradation of streaming quality due to low-achieving throughput (i.e., lower throughput than the maximum throughput that a streaming flow requires in maximum audio/video quality) and data packet losses. GENEVA avoids this problem by allowing a streaming flow to maintain moderate network congestion while trying to recover lost data packets that other competing flows cause during the process of probing for available bandwidth. Using the GMIAD mechanism, the FEC window size (the degree of FEC redundancy per unit time) is adjusted to suppress occurrences of bursty packet loss, while trying to effectively utilize network resources that other competing flows cannot consume due to reductions in the transmission rate in response to packet loss. We describe the GENEVA algorithm and evaluate its effectiveness using an NS-2 simulator. The results show that GENEVA enables high-performance streaming flows to retain higher streaming quality under stable conditions while minimizing the adverse impact on competing TCP performance.