In this paper, we propose a nonlinear control model to characterize the AQM algorithm-GREEN. Based on this model, we analyze its performance and prove that there exists a stable oscillation when in equilibrium. Furthermore, we also investigate the effects of the factors such as bandwidth, round trip time, and load level on the amplitude and frequency of the oscillation. Theoretical analysis and simulation results indicate that GREEN algorithm is insensitive to the network conditions when the link rate and the round trip time are relatively small and becomes more sensitive to the change of network conditions when the bandwidth delay product is relatively high. For GREEN the adaptability to a wide range of network conditions is based on the compromising of the efficiency.

In this paper, we propose a scalable Extended Differentiated-Services (EDS) architecture to guarantee edge-to-edge explicit rate allocation. In presence of flows with explicit rate allocation, to share bandwidth fairly, a new fairness definition is proposed. Based on EDS and the proposed fairness definition, a scalable fair Edge-to-Edge Congestion Control Algorithm with Explicit Rate Allocation (ECC-ERA) is presented to solve the bandwidth assurance problem facing Differentiated Service architecture, where EDS uses congestion control packets to carry the flow-related states and congestion control information. By designing efficiency control and fairness control separately, the ECC-ERA can achieve good scalability to link capacity, round-trip time and number of flows. It will be shown that EDS plus ECC-ERA outperforms the general Diff-Serv bandwidth guarantee approaches. The main advantages of EDS+ECC-ERA are as follows: (1) it not only can guarantee explicit rate allocation, but also can guarantee near-zero packet loss in core routers, high utilization, lower and smoother queueing delay, better fairness and better protection from unresponsive traffic. (2) Neither resource pre-reservation nor sophisticated scheduling mechanisms are required. The simple FIFO at core routers is enough. (3) EDS plus EC-ERA is very efficient and can be used as end-to-end QoS building block.