  In this note we analyse various stability properties of the max-min fair Rate
Control Protocol (RCP) operating with small buffers. We first tackle the issue
of stability for networks with arbitrary topologies. We prove that the max-min
fair RCP fluid model is globally stable in the absence of propagation delays,
and also derive a set of conditions for local stability when arbitrary
heterogeneous propagation delays are present. The network delay stability
result assumes that, at equilibrium, there is only one bottleneck link along
each route. Lastly, in the simpler setting of a single link, single delay
model, we investigate the impact of the loss of local stability via a Hopf
bifurcation.
