In this paper we use a previously developed RED (random early detection) model to analyze and develop a quantitative approach of defining one of the RED parameters, average queue weight, while the network load level varies. First, we introduce the linear control system and the pre-developed RED model. Based on this model, we next develop a proposition aiming at the RED parameter, average queue weight, and the load level only, to ensure the system stay stable. Our research is intended to provide a quantitative basis for parameterizing RED while load level varies. We present ns simulations to support our analysis