Using Fisher information to assess stability in the performance of public transportation systems

Public transportation systems (PTS) are large and complex systems that consist of many modes operated by different agencies to service entire regions. Assessing their performance can therefore be difficult. In this work, we use concepts of Fisher information (FI) to analyse the stability in the performance of PTS in the 372 US urbanized areas (UZA) reported by the National Transit Database. The key advantage of FI is its ability to handle multiple variables simultaneously to provide information about overall trends of a system. It can therefore detect whether a system is stable or heading towards instability, and whether any regime shifts have occurred or are approaching. A regime shift is a fundamental change in the dynamics of the system, e.g. major and lasting change in service. Here, we first provide a brief background on FI and then compute and analyse FI for all US PTS using monthly data from 2002 to 2016; datasets include unlinked passenger trips (i.e. demand) and vehicle revenue miles (i.e. supply). We detect eight different patterns from the results. We find that most PTS are seeking stability, although some PTS have gone through regime shifts. We also observe that several PTS have consistently decreasing FI results, which is a cause for concern. FI results with detailed explanations are provided for eight major UZA.