Linear time-delay system model and stability of AQM bottleneck networks

Active queue manage networks belong to nonlinear large scale systems. There are many uncertain factors such access number of subscribers, traffic types, link capacities and round trip time, impact on the networkspsila behaviors. However, the existing nonlinear fluid models for AQM networks have not considered the hybrid traffic flows: TCP/UDP ones, they only are valid for TCP traffic flows. This paper establishes a general linear time-delay model for the bottleneck networks with TCP/UDP AQM, considering the uncertainty of access number of subscribers, traffic types, link capacities and round trip time. The proposed time-delay system model is derived from linearization processing for fluid-based model at equilibrium points. Resort to the time-delay system model, the stability analysis of the AQM networks with uncertainty can be analyzed in 2-D s-z domain. At equilibrium points, the bottleneck networks are described by uncertain linear time-delay systems, then 2-D (two-dimensional) Laplace-z transform has been applied for the stability test of the network. The stability implies the congestion conditions of the AQM networks. Simulations verify the stability analysis for AQM network to be valid, the AQM network approaches to full utilization without PI controller of.