Stability and bifurcation analysis of the AVQ and E-RED queue management policies

We analyze some local stability and Hopf bifurcation properties of the Adaptive Virtual Queue (AVQ) and the Exponential-RED (E-RED) queue policy. Using a fluid model for flow control, coupled with these queue management policies, we first determine the necessary and sufficient conditions for local stability. Then, for both queue policies, we show that the underlying coupled system undergoes a Hopf bifurcation. Further, for the E-RED policy, using Poincaré normal forms and the center manifold theory, we outline an analytical basis to determine the asymptotic orbital stability of the emerging limit cycles. Finally, using packet-level simulations we highlight that the existence of limit cycles leads to a loss in link utilization. Such limit cycles can hurt network performance and should be avoided. Some stability charts, and numerical computations, complement our analysis.