Fairness and convergence results for additive-increase multiplicative-decrease multiple-bottleneck networks

We examine the behavior of the additive-increase multiplicative-decrease (AIMD) congestion control algorithm. We present a variant of a proposed matrix model that allows us to obtain previous results for competition via a single bottleneck link. We then extend these results to the case of multiple bottleneck links paying particular attention to some aspects of fairness and convergence properties for multiple bottleneck systems. We examine both the synchronous (deterministic) and asynchronous (stochastic) cases. A simple simulation example illustrates the results.