This paper presents a control-theoretic approach to reactive flow control in networks that do not reserve bandwidth. We assume a round-robin-like queue service discipline in the output queues of the network's switches, and propose deterministic and stochastic models for a single conversation in a network of such switches. These models motivate the Packet-Pair rate probing technique, and a provably stable rate-based flow control scheme. A Kalman state estimator is derived from discrete-time state space analysis, but there are difficulties in using the estimator in practice. These difficulties are overcome by a novel estimation scheme based on fuzzy logic. We then present a technique to extract and use additional information from the system to develop a continuous-time system model. This is used to design a variant of the control law that is also provably stable, and, in addition, takes control action as rapidly as possible. Finally, practical issues such as correcting parameter drift and coordination with window flow control are described.