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Given the ubiquitous nature of infrastructure networks in today's society, there is a global need to understand, quantify, and plan for the resilience of these networks to disruptions. This work defines network resilience along dimensions of reliability, vulnerability, survivability, and recoverability, and quantifies network resilience as a function of component and network performance. The treatment of vulnerability and recoverability as random variables leads to stochastic measures of resilience, including time to total system restoration, time to full system service resilience, and time to a specific α% resilience. Ultimately, a means to optimize network resilience strategies is discussed, primarily through an adaption of the Copeland Score for nonparametric stochastic ranking. The measures of resilience and optimization techniques are applied to inland waterway networks, an important mode in the larger multimodal transportation network upon which we rely for the flow of commodities. We provide a case study analyzing and planning for the resilience of commodity flows along the Mississippi River Navigation System to illustrate the usefulness of the proposed metrics.