Stability and bifurcation analysis of Westwood+ TCP congestion control model in mobile cloud computing networks

Abstract

In this paper, we first build up a Westwood+ TCP congestion control model with communication delay in mobile cloud computing networks. We then study the dynamics of this model by analyzing the distribution ranges of eigenvalues of its characteristic equation. Taking communication delay as the bifurcation parameter, we derive the linear stability criteria depending on communication delay. Furthermore, we study the direction of Hopf bifurcation as well as the stability of periodic solution for the Westwood+ TCP congestion control model with communication delay. We find that the Hopf bifurcation occurs when the communication delay passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by the normal form theory and the center manifold theorem. Finally, numerical simulation is done to verify the theoretical results.

Evolutionary dynamics of the delayed replicator-mutator equation: Limit cycle and cooperation

“…Thus, one can say that the stability of a fixed point in the presence of delay is solely determined by the eigenvalue, λ 0 , corresponding to the principal branch of the Lambert W function. We expect emergence of stable limit cycle as a consequence of Hopf bifurcation about a fixed point when it has purely imaginary λ 0 and all other eigenvalues are such that Re(λ k ) < 0 [55][56][57][58][59].…”