In this paper, we analyze a model for transport control protocol (TCP) along with a non-adaptive virtual queue (VQ) and an adaptive virtual queue (AVQ) management policy. In the class of transport protocols, we focus on compound TCP as it is the default protocol in the Windows operating system. We start by conducting a local stability analysis for the underlying fluid models. For the VQ policy, we show that small virtual buffers play an important role in ensuring stability, whereas the AVQ policy could readily lose local stability as the link capacity, the feedback delay, or the link's damping factor gets large. With both the queue policies, the protocol parameters of compound TCP also influence stability. Furthermore, in both the models, we explicitly show that as parameters vary the loss of local stability would occur via a Hopf bifurcation. For the AVQ policy, we are also able to analytically verify if the Hopf bifurcation is super-critical, and determine the stability of the bifurcating limit cycles. Packet-level simulations, conducted over two topologies, using the network simulator (NS2) confirm the existence of stable limit cycles in the queue size.