  The AIMD algorithm, which underpins the Transmission Control Protocol (TCP)
for transporting data packets in communication networks, is perhaps the most
successful control algorithm ever deployed. Recently, its use has been extended
beyond communication networks, and successful applications of the AIMD
algorithm have been reported in transportation, energy, and mathematical
biology. A very recent development in the use of AIMD is its application in
solving large-scale optimization and distributed control problems without the
need for inter-agent communication. In this context, an interesting problem
arises when multiple AIMD networks that are coupled in some sense (usually
through a nonlinearity). The purpose of this note is to prove that such systems
in certain settings inherit the ergodic properties of individual AIMD networks.
This result has important consequences for the convergence of the
aforementioned optimization algorithms. The arguments in the paper also correct
conceptual and technical errors in [1].
