The impact of data characteristics on the estimation of the three-dimensional passenger macroscopic fundamental diagram

The three-dimensional passenger macroscopic fundamental diagram (pMFD) defines the functional relation between car accumulation, bus accumulation, and travel production of passengers. It facilitates the analysis of bi-modal traffic dynamics from the perspective of passenger flows. Usually, it is estimated based on empirical or simulated data. This paper focuses on the role of data characteristics for such a data-based estimation. Thereby, we study two main scenarios: First, we examine the effects of penetration and sampling rates, as well as speed measurement errors of person-specific position data on the pMFD estimation. Second, we study the estimation accuracy assuming that only data from automatic passenger count (APC) devices and loop detectors are available. This reflects a more realistic data source for local authorities. In this context, we investigate the impact of the penetration rate of APC device-equipped buses on the pMFD estimation. To quantify the impact of those aspects, we compare the resulting pMFDs to the ground truth pMFD, which has a penetration rate of 100 %, a sampling rate of 1 Hz, and no error in the speed data. To reduce the case dependency, we conduct this analysis for two networks: the well-known Sioux Falls network, and Schwabing, a district in Munich, Germany. The results of our study show that the penetration rate has a strong influence on the pMFD and the error increases faster the lower the penetration rate is. In contrast, the sampling rate and speed measurement error have a smaller impact on the pMFD estimation. Additionally, our results indicate that the estimation accuracy is reasonably high when APC data is utilized. The results of this study are relevant to both scientists and practitioners, as we not only advance the knowledge on the pMFD estimation but also show what data are necessary for robust estimation and thus its application in practice.