  We study the interaction between the AIMD (Additive Increase Multiplicative
Decrease) congestion control and a bottleneck router with Drop Tail buffer. We
consider the problem in the framework of deterministic hybrid models. First, we
show that the hybrid model of the interaction between the AIMD congestion
control and bottleneck router always converges to a cyclic behavior. We
characterize the cycles. Necessary and sufficient conditions for the absence of
multiple jumps of congestion window in the same cycle are obtained. Then, we
propose an analytical framework for the optimal choice of the router buffer
size. We formulate the problem of the optimal router buffer size as a
multi-criteria optimization problem, in which the Lagrange function corresponds
to a linear combination of the average goodput and the average delay in the
queue. The solution to the optimization problem provides further evidence that
the buffer size should be reduced in the presence of traffic aggregation. Our
analytical results are confirmed by simulations performed with Simulink and the
NS simulator.
