Stability and Sensitivity Analysis of Traffic-Shaping Algorithms Inspired by Chemical Engineering

摘要

Traffic-shaping algorithms, such as congestion avoidance or rate limiting for cloud services, control the dynamics of packet flows in a distributed setting. However, despite their significance in networking, it is still hard to design them, to predict their dynamic behavior, and to prove their robustness. With the help of a simple chemical metaphor, we recently proposed a novel engineering framework for designing, executing, and analyzing traffic-shaping algorithms: by letting packets react akin to chemical molecules, the design of (distributed) flow-control algorithms becomes drawing reaction networks. In this way, we gain in analyzability: the related fluid model, describing the emergent behavior of the overall system, can be derived from the corresponding reaction networks automatically. In this article, we describe how to fine-tune chemical algorithms. We therefore analyze their transient behavior in order to reveal the semantics and sensitivity of key parameters. Methods from different domains assist us in this endeavor: We first linearize the fluid model as proposed in Metabolic Control Analysis, we then describe it in control-theoretic terms, and finally, we characterize its sensitivity in the frequency domain. We demonstrate the feasibility and reveal the limits of our method by applying it to a chemical algorithm for distributed rate control.