Public transport across models and scales: A case study of the Munich network.

The use of public transport systems is a striking example of complex human behavior. Modeling, planning, and managing public transport is a major future challenge considering the drastically accelerated population growth in many urban areas. The desire to design sustainable cities that can cope with a dynamically increasing demand requires models for transport networks since we are not able to perform real-life experiments before constructing additional infrastructure. Yet, there is a fundamental challenge in the modeling process: we have to understand which basic principles apply to the design of transit networks. In this work, we are going to compare three scientific methods to understand human behavior in public transport modeling: agent-based models, centralized optimization-based models, and minimal physics-based models. As a case study, we focus on the transport network in Munich, Germany. We show that there are certain universal macroscopic emergent features of public transport that arise regardless of the model chosen. In particular, we can obtain with minimal basic assumptions a common and robust distribution for the individual passenger in-vehicle time as well as for several other distributions. Yet, there are other more microscopic features that differ between the individual and centralized organization and/or that cannot be reproduced by a minimal nonlocal random-walk type model. Finally, we cross-validate our results with observed public transport data. In summary, our results provide a key understanding of the basic assumptions that have to underlie transport modeling for human behavior in future sustainable cities.