Recent research reveals that the fluid-based model can describe the dynamic behavior for bottleneck networks. The stability of the fluid-based model can inflect whether there exists a congestion of the network. This paper develops a linearization processing for fluid-based model at equilibrium points for the stability analysis of the networks with Active Queue Management (AQM). The bottleneck networks are described by uncertain linear time-delay systems, then 2-D (two-dimensional) Laplace-z transform has been applied in the stability test of the network. Simulations verify the stability analysis for AQM network to be valid, the AQM network approaches to full utilization, while the buffer size on the order of bandwidth-delay product is necessary for the stability of the fluid model with full utilization.