Deterministic and stochastic convergence properties of AIMD algorithms with nonlinear back-off functions

In this paper we establish basic stability results for a class of nonlinear AIMD (additive-increase multiplicative-decrease) algorithms. We consider networks in which the nonlinearity enters through the multiplicative-decrease mechanism. In particular, where the multiplicative-decrease function depends in a nonlinear fashion on the achieved rate. For synchronized deterministic networks, we establish stability and convergence results. For non-synchronized stochastic networks, basic convergence results are also established. In particular, we give conditions for the existence of a unique invariant stationary distribution, and conditions under which time- and ensemble-averages converge to the same unique value (irrespective of initial conditions).