One of the challenges in the design of switches/routers is the efficient and fair use of the shared bottleneck bandwidth among different Internet flows. In particular, various active queue management (AQM) schemes have been developed to regulate transmission control protocol traffic in response to router congestion. In addition, in order to provide fair bandwidth sharing, these AQM must protect the well-behaved flows from the misbehaving flows. However, most of the existing AQM schemes cannot provide accurate fair bandwidth sharing while being scalable. The key to the scalability and fairness of the AQM schemes is the accurate estimation of certain network resources without keeping too much state information. We propose a novel technique to estimate two network resource parameters: the number of flows in the buffer and the data source rate of a flow by using a capture-recapture (CR) model. The CR model depends on simply the random capturing/recapturing of the incoming packets, and as a result, it provides a good approximation tool with low time/space complexity. These network resource parameters are then used to provide fair bandwidth sharing among the Internet flows. Our experiments and analysis will demonstrate that this new technique outperforms the existing mechanisms and closely approximates the "ideal" case, where full state information is needed.