The Rate Control Protocol (RCP) uses explicit feedback from routers to control network congestion. RCP estimates it's fair rate from two forms of feedback: rate mismatch and queue size. An important design question that remains open in RCP is whether the presence of queue size feedback is helpful, given the presence of feedback from rate mismatch. The feedback from routers to endsystems is time delayed, and may introduce instabilities and complex non-linear dynamics. Delay dynamical systems are often modeled using delay differential equations to facilitate a mathematical analysis of their performance and dynamics. The RCP models with and without queue size feedback give rise to two distinct non-linear delay differential equations. Earlier work on this design question was based on methods of linear systems theory. For further progress it is quite natural to employ nonlinear techniques. In this study, we approach this design question using tools from control and bifurcation theory. The analytical results reveal that the removal of queue feedback could enhance both stability and convergence properties. Further, using Poincaré normal forms and center manifold theory, we investigate two nonlinear properties, namely, the type of Hopf bifurcation and the asymptotic stability of the bifurcating limit cycles. We show that the presence of queue feedback in the RCP can lead to a sub-critical Hopf bifurcation, which would give rise either to the onset of large amplitude limit cycles or to unstable limit cycles. Whereas, in the absence of queue feedback, the Hopf bifurcation is always super-critical and the bifurcating limit cycles are stable. The analysis is complemented with computations and some packet-level simulations as well. In terms of design, our study suggests that the presence of both forms of feedback may be detrimental to the performance of RCP.
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, given the presence of feedback based on rate mismatch. To address this question, we conduct analysis (stability and Hopf bifurcation) and packet-level simulations. The analytical results reveal that the presence of queue size feedback in the protocol specification may induce a sub-critical Hopf bifurcation, which can lead to undesirable system behavior. The analysis is corroborated by numerical computations and some packet-level simulations. Based on our work, the suggestion for RCP is to only include feedback based on rate mismatch in the design of the protocol.
The Rate Control Protocol (RCP) is a congestion control protocol that relies on explicit feedback from routers. RCP estimates the flow rate using two forms of feedback: rate mismatch and queue size. However, it remains an open design question whether queue size feedback in RCP is useful, given the presence of rate mismatch. The model we consider has RCP flows operating over a single bottleneck, with heterogeneous time delays. We first derive a sufficient condition for global stability, and then highlight how this condition favors the design choice of having only rate mismatch in the protocol definition.
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