Global stability of the Rate Control Protocol (RCP) and some implications for protocol design

Abstract Global stability is an important aspect associated with the analysis and performance of closed-loop systems with feedback delays. The presence of time delays in the feedback makes the system infinite-dimensional. Establishing conditions for global stability of delay models is a non-trivial task when the system is non-linear, and the feedback delays are heterogeneous. In this paper, at the level of theoretical interest, we first derive a simply stated sufficient condition for the global asymptotic stability for a non-linear delay differential equation with heterogeneous time delays. We then apply the analytical results to the Rate Control Protocol (RCP), which is a congestion control protocol that relies on explicit feedback from routers. We establish that RCP can be made globally asymptotically stable - an important property of the algorithm previously unknown. We are able to deduce a condition for global stability of RCP, in the presence of heterogeneous feedback delays. The condition for stability favors the design choice of having only rate mismatch, as opposed to both rate mismatch and queue size, in the protocol definition. The analysis is corroborated with some numerical simulations.