In this work, a prescribed finite time active queue management scheme for congestion control in IP networks is proposed to address the challenges of time delay and input saturation. A delay compensation-based predictor is utilized to eliminate input delay, and a novel nonlinear anti-windup compensator is constructed to handle input saturation. The proposed scheme is composed of two parts: the first one designs a predicted state-based active queue management scheme without considering saturation, and the second one develops a nonlinear anti-windup compensator to address saturation issues. The combination of these two results ensures prescribed finite-time stabilization even when the input is subject to saturation. The effectiveness of the proposed Prescribed Active Queue Management (PrAQM) scheme is demonstrated through simulations on a dumbbell network topology.