The Physical Internet (PI) paradigm, which has gained attention in research and academia in recent years, leverages advanced logistics and interconnected networks to revolutionise the way goods are transported and delivered, thereby enhancing efficiency, reducing costs and delays, and minimising environmental impact. Within this system, PI-hubs function similarly to cross-docks, enabling the splitting of PI-containers into smaller modules for delivery through a network of interconnected hubs. This allows dynamic routing optimisation and efficient consolidation of PI-containers. However, the impact of system parameters and 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 logistics framework is affected by the handling, consolidation, and processing of PI-containers at PI-hubs. To this end, the considered PI logistics 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-hub processing times and the number of modules per PI-container. In particular, a Global Sensitivity Analysis (GSA) is performed to evaluate, through a case study, the individual relevance of each input parameter on the resulting performance.