Data-driven bus timetabling with spatial-temporal travel time

Travel time at inter-stops is a set of important parameters in bus timetabling, which is usually assumed to be normal (log-normal) random variable in literature. With the development of digital technology and big data analytics ability in the bus industry, practitioners prefer to generate deterministic travel time based on the on-board GPS data under maximum probability rule and mean value rule, which simplifies the optimization procedure, but performs poorly in the timetabling practice due to the loss of uncertain nature on travel time. The purpose of this study is to propose a GPS-data-driven bus timetabling approach with consideration of the spatial-temporal characteristic of travel time.

The authors illustrate that the real-life on-board GPS data does not support the hypothesis of normal (log-normal) distribution on travel time at inter-stops, thereby formulating the travel time as a scenario-based spatial-temporal matrix, where K-means clustering approach is utilized to identify the scenarios of spatial-temporal travel time from daily observation data. A scenario-based robust timetabling model is finally proposed to maximize the expected profit of the bus carrier. The authors introduce a set of binary variables to transform the robust model into an integer linear programming model, and speed up the solving process by solution space compression, such that the optimal timetable can be well solved by CPLEX.

Case studies based on the Beijing bus line 628 are given to demonstrate the efficiency of the proposed methodology. The results illustrate that: (1) the scenario-based robust model could increase the expected profits by 15.8% compared with the maximum probability model; (2) the scenario-based robust model could increase the expected profit by 30.74% compared with the mean value model; (3) the solution space compression approach could effectively shorten the computing time by 97%.

This study proposes a scenario-based robust bus timetabling approach driven by GPS data, which significantly improves the practicality and optimality of timetable, and proves the importance of big data analytics in improving public transport operations management.