In this paper, a new effective and computationally reduced method for congestion control in high speed dynamic computer networks is introduced. The controller is designed using the well-known predictive functional control (PFC) scheme and an ARMarkov model representation that considers the system delay explicitly. Use of the multi-step-ahead predictive ARMarkov model structure within the PFC results in a simple algebraic control law that does not require recursive model output computation in the so-called prediction horizon performed in the other Model Predictive Controllers (MPC). This combination not only reduces the required computational load, but the accumulative error due to the model uncertainties decrease considerably. Packet-level simulations based on ns-2 are provided to show good performance of ARM-PFC in a large variety of topology and traffic mixtures for both queue regulation and resource utilization. Fast response, low queue fluctuations (and consequently low delay and jitter), high link utilization, good disturbance rejection, scalability, and low packet marking probability are other features of the proposed method with respect to the well-known AQM methods such as RED, PI, and REM, which are also simulated for comparison.