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The term capacity has natural connotations about fundamental limits and robustness to disruptions. For engineered systems, a rigorous characterization of capacity also provides insight into algorithms with universal performance guarantees and informs optimal strategic resource allocation. We present analysis and optimization of capacity and related performance metrics for societal cyber-physical systems (including traffic, mobility, and power networks) in canonical settings. At the macroscopic scale, we extend static network flow formulations to several flow dynamics and control settings (including cascading failure). The tractability of the resulting nonlinear analysis and optimization is facilitated by the spatial sparsity of dynamics and invariance of key input-output properties, such as monotonicity, across multiple resolutions in the network. At the microscopic scale, we consider spatial queues with state-dependent service rate; for example, such problems arise in networks of dynamically coupled vehicles. While this dependence is complex in general, we provide tight characterization in limiting cases, for instance large queue length, which leads to tight throughput estimates. Case studies are provided to evaluate the effectiveness of the proposed frameworks.