Fluid Model of an Internet Router under the Mimd Control Scheme

We study the interaction between an MIMD (Multiplicative Increase Multiplicative Decrease) congestion control algorithm and a Drop Tail buffer. We consider the problem in the framework of deterministic hybrid models. We first show that the hybrid model of the interaction between the MIMD congestion control and bottleneck router always converges to a cyclic behavior that can be of only two different types. Second, we characterize the minimum buffer size required such that the bottleneck link is fully utilized. In particular, our analysis indicates that an MIMD algorithm requires smaller buffer sizes than AIMD in order to fully utilize the link capacity.