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As CDMA-based cellular networks mature, the current point-to-point links used in connecting base stations to network controllers will evolve to an IP-based radio access network (RAN) for reasons of lower cost due to statistical multiplexing gains, better scalability and reliability, and the projected growth in data applications. In this paper, we study the impact of congestion in a best-effort IP RAN on CDMA cellular voice networks. We propose and evaluate three congestion control mechanisms, admission control, diversity control, and router control, to maximize network capacity while maintaining good voice quality. We first propose two new enhancements to CDMA call admission control that consider a unified view of both IP RAN and air interface resources. Next, we introduce a novel technique called diversity control that exploits the soft-handoff feature of CDMA networks and drops selected frames belonging to multiple soft-handoff legs to gracefully degrade voice quality during congestion. Finally, we study the impact of router control where an active queue management technique is used to reduce delay and minimize correlated losses. Using simulations of a large mobile network, we show that the three different control mechanisms can help gracefully manage 10-40% congestion overload in the IP RAN.