High-performance networks are based on one of two architectures, namely, the Integrated Services Architecture (ISA) and the Differentiated Service Architecture (DiffServ). In order to provide different qualities of service to different flows, or aggregates of flows, different scheduling mechanisms are used at routers, in addition to the employment of queue management technique. This thesis considers the modeling of active queue management techniques, and in particular the RED with IN and OUT (RIO) mechanism. The model is based on a discrete time stochastic model using a two- dimensional, second-order Markov chain. In order to capture the features of RIO, two levels of Markov process modeling are used: a microscopic level, at the packet transmission time boundaries, and a macroscopic level, at the start of the new round trip time. Several performance measures are derived, and numerical results are compared to the results from the OPNET simulator, which is used to assess the accuracy of the model. This thesis also introduces a strategy for the selection of the maximum threshold selection in the RED algorithm, which can be extended to RIO and other active queue management techniques using thresholds. The OPNET simulator is also used to verify the correctness of this strategy.