Meaningful Modeling of Section Bus Running Times by Time Varying Mixture Distributions of Fixed Components

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, place - urban, operations - scheduling, operations - reliability, operations - performance


Bus travel, Distributions (Statistics), Periods of the day, Running time, Travel time, Urban transportation


Understanding the variability of bus travel time is a key issue in the optimization of schedules, transit reliability, route choice analysis, and transit simulation. The statistical modeling of bus travel time data is of increasing importance given the increasing availability of data.

In this paper, we introduce a novel approach to modeling the day-to-day variability of urban bus running times on a section level. First, the explanatory power of conventionally used distributions is examined, based on likelihood and effect size. We show that a mixture model is a powerful tool to increase fitting performance, but the applied components need to be justified. To overcome this issue, we propose a novel model consisting of two individual characteristic distributions representing either off-peak or peak hour dynamics. The observed running time distribution at every hour of the day can be described as a combination (mixture) of the two dynamics. The proposed time varying model uses a small set of parameters, which are physically interpretable and capable of accurately describing running time distributions. With our modeling approach, we reduce the complexity of mixture models and increase the explanatory power and fit compared with conventional models.


Permission to publish the abstract has been given by SAGE, copyright remains with them.