On the stability and multi-stability of a TCP/RED congestion control model with state-dependent delay and discontinuous marking function

Random early detection (RED) is an effective algorithm to control the Internet congestion. However, researches on RED parameters are difficult since there are state-dependent delay and discontinuous terms on the right-hand side of the model. We smooth the model by hyperbolic tangent function and reformulate it by a switch function to keep state variables positive. Numerical simulations on the original system validates the reformulated model. The multi-stability phenomenon is observed and some suggestions on the selection of RED parameters are given to enhance the global stability of the model by numerical bifurcation continuation on the reformulated model.