  There is considerable interest in the networking community in explicit
congestion control as it may allow the design of a fair, stable, low loss, low
delay, and high utilization network. The Rate Control Protocol (RCP) is an
example of such a congestion control protocol. The current design of RCP
suggests that it should employ two forms of feedback; i.e. rate mismatch and
queue size, in order to manage its flow control algorithms. An outstanding
design question in RCP is whether the presence of queue size feedback is useful
or not, given feedback based on rate mismatch. In this paper, we address this
question using tools from control and bifurcation theory. We linearize the
actual non-linear system and analyze the local asymptotic stability, robust
stability and rate of convergence of both the design choices, i.e., with and
without queue size feedback. But such analyses do not offer clear design
recommendations on whether the queue feedback is useful or not. This motivates
a bifurcation-theoretic analysis where we have to take non-linear terms into
consideration, which helps to learn additional dynamical properties of the RCP
system. In particular, we proceed to analyze two non-linear properties, namely,
the type of Hopf bifurcation and the asymptotic stability of the bifurcating
limit cycles. Analytical results reveal that the presence of queue feedback in
RCP can induce a sub-critical Hopf bifurcation, which can lead to undesirable
system behavior. Whereas, in the absence of queue feedback, the Hopf
bifurcation is always super-critical where the bifurcating limit cycles are
stable and of small amplitude. The analysis is corroborated by numerical
computations and some packet-level simulations as well. Based on our work, the
suggestion for RCP is to only include feedback based on rate mismatch in the
design of the protocol.
