Virtual queue-based active queue management schemes have been proposed to provide low-loss, low-delay service in the Internet. In an earlier work, we had proposed a particular scheme called the adaptive virtual queue (AVQ) algorithm where the capacity of the virtual queue is adapted to the traffic conditions to achieve a desired level of utilization in the network. Here, we study the choice of the parameters of the congestion-controllers at the sources and the AVQ scheme at the links that is required to ensure stability. In particular, we consider a system in which users with diverse round-trip delays and fairness requirements access a general topology network. For this system, we show that, by choosing the speed of adaptation at the sources and the links appropriately, one can guarantee the stability of the network.