Local Hopf bifurcation analysis of Compound TCP with an Exponential-RED queue management policy

The analysis of TCP, along with queue management policies, forms an important aspect of performance evaluation for the Internet. In this paper, we analyse a non-linear fluid model for Compound TCP (C-TCP) coupled with an Exponential-RED (E-RED) queue management policy. Compound is an important flavor of TCP, as it is the default transport protocol in the Windows operating system. For the bifurcation analysis, we motivate an exogenous and non-dimensional bifurcation parameter. Using this parameter, we first derive the Hopf bifurcation condition for the underlying model. Then, employing Poincaré normal forms and the center manifold theory, we outline the analysis to characterise the type of the Hopf bifurcation, and determine the stability of the bifurcating periodic solutions. Some numerical analysis and stability charts complement our theoretical analysis.