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Rate Control Protocol (RCP) uses feedback from routers to assign flows theirfair rate. RCP estimates the fair rate using two forms of feedback: ratemismatch and queue size. An outstanding design question for RCP is whether thequeue size feedback is useful or not. To address this, we analyze stability andthe bifurcation properties of RCP in both the cases i.e., with and withoutqueue size feedback. The model considers flows with two different round-triptimes, operating over a single bottleneck link. By using an exogenousbifurcation parameter, we show that the system loses stability via a Hopfbifurcation and hence we can expect a limit cycle branching from the fixedpoint. We highlight that the presence of queue feedback can readily destabilizethe system. Using Poincar{\`e} normal forms and the center manifold theorem, weshow that the Hopf bifurcation is super-critical in the case of RCP withoutqueue feedback. Whereas, in the presence of queue feedback, we show that thesystem can undergoes a sub-critical Hopf bifurcation for some parameter values.A sub-critical Hopf bifurcation can result in either large amplitude limitcycles or unstable limit cycles, and hence should be avoided in engineeringapplications. Thus, the presence of queue feedback would create adverse effectson the stability of the emerging limit cycles. In essence, the analyticalresults of RCP with two delays favor the design choice that uses feedback basedonly on rate mismatch. The theoretical analysis is validated with numericalcomputations and some packet level simulations as well.

Impact of queue feedback on the stability and dynamics of a Rate Control Protocol (RCP) with two delays