Hopf bifurcation analysis for congestion control with heterogeneous delays (Q984597)

The paper analyses a system of three differential equations with delay, which models congestion control with the random exponential marking algorithm and round trip delays. The authors first linearize in the unique non-trivial steady state and classify its stability depending on a single system parameter, finding a Hopf bifurcation. Finally, the Hopf criticality is calculated in the usual way, resulting in a formula which is, as usual, too complicated to give any insight without inserting numerical values. Some numerical simulations confirm the prediction obtained by the formula.