Critical transportation infrastructure has been studied extensively in recent years. This paper presents a spatiotemporal analysis of critical transportation links based on time geographic concepts. With widespread adoption of information and communication technologies (ICT) and location-aware mobile devices, large tracking datasets have become readily available. This study uses a tracking dataset of approximately 12,000 taxis in Wuhan, China over 1 week to analyze spatiotemporal origin–destination (O–D) patterns of trips that use three critical bridges connecting the three districts of Wuchang, Hankou, and Hanyang separated by the Yangtze River and the Han River. We use the space–time prism concept to identify alternative space–time paths passing through different bridges that observe the spatial and temporal constraints between each O–D pair derived from the taxi trajectory data. This case study illustrates the feasibility and benefits of using the proposed time geographic approach to analyze spatiotemporal patterns of travel demands on the critical links and their alternative paths in a transportation system.