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The conventional view of the congestion control problem in data networks is based on the principle that a flow's performance is uniquely determined by the state of its bottleneck link, regardless of the topological properties of the network. However, recent work has shown that the behavior of congestion-controlled networks is better explained by models that account for the interactions between bottleneck links. These interactions are captured by a latent \textit{bottleneck structure}, a model describing the complex ripple effects that changes in one part of the network exert on the other parts. In this paper, we present a \textit{quantitative} theory of bottleneck structures (QTBS), a mathematical and engineering framework comprising a family of polynomial-time algorithms that can be used to reason about a wide variety of network optimization problems, including routing, capacity planning and flow control. QTBS can contribute to traffic engineering by making clear predictions about the relative performance of alternative flow routes, and by providing numerical recommendations for the optimal rate settings of traffic shapers. A particularly novel result in the domain of capacity planning indicates that previously established rules for the design of folded-Clos networks are suboptimal when flows are congestion controlled. We show that QTBS can be used to derive the optimal rules for this important class of topologies, and empirically demonstrate the correctness and efficacy of these results using the BBR and Cubic congestion-control algorithms.