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The Physical Internet (PI) paradigm, which has gained attention in research and academia in recent years, leverages advanced logistics and interconnected networks to revolutionize the way goods are transported and delivered, thereby enhancing efficiency, reducing costs and delays, and minimizing environmental impact. Within this system, PI-hubs function similarly to cross-docks enabling the splitting of PI-containers into smaller modules to be delivered through a network of interconnected hubs, allowing dynamic routing optimization and efficient consolidation of PI-containers. Nevertheless, the impact of the system parameters and of the relevant uncertainties on the performance of this innovative logistics framework is still unclear. For this reason, this work proposes a robustness analysis to understand how the PI logistic framework is affected by how PI-containers are handled, consolidated, and processed at the PI-hubs. To this end, the considered PI logistic system is represented via a mathematical programming model that determines the best allocation of PI-containers in an intermodal setting with different transportation modes. In doing so, four Key Performance Indicators (KPIs) are separately considered to investigate different aspects of the PI system's performance and the relevant robustness is assessed with respect to the PI-hubs' processing times and the number of modules per PI-container. In particular, a Global Sensitivity Analysis (GSA) is considered to evaluate, by means of a case study, the individual relevance of each input parameter on the resulting performance.