Modeling conditional dependencies for bus travel time estimation

In the age of Intelligent Transportation Systems it is essential to provide operators and passengers with reliable information. The estimation of probability distributions of public transport travel times is crucial as it directly informs about the reliability of travel times. Thus, the probability distributions of travel times are useful for timetabling and route choice. This work estimates probability distributions of segment (multi-section) bus running and dwell times. We propose a hidden Markov chain framework, which captures the dependency structure of consecutive section running times and includes conditional correlations. The dependency structure of consecutive segment dwell times is modeled as a combination of correlation and operation-specific dependencies. Such a model allows describing the relationship between section-level running/station-level dwell time distributions and segment level distributions. The model is interpretable, as the dependency structure is explicitly modeled. Finally, the proposed model is evaluated on the operation of the trolley bus network of Zurich, Switzerland, and shows an average increase in fitting quality (measured by Wasserstein distance) of 26% for running times and 29% for dwell times compared to an approach not including conditional dependencies, i.e., convolution of link running and dwell times.