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Accurate forecasting of bus travel time and its uncertainty is critical to service quality and operation of transit systems; for example, it can help passengers make better decisions on departure time, route choice, and even transport mode choice and also support transit operators to make informed decisions on tasks such as crew/vehicle scheduling and timetabling. However, most existing approaches in bus travel time forecasting are based on deterministic models that provide only point estimation. To this end, we develop in this paper a Bayesian probabilistic forecasting model for bus travel time. To characterize the strong dependencies/interactions between consecutive buses, we concatenate the link travel time vectors and the headway vector from a pair of two adjacent buses as a new augmented variable and model it with a constrained Multivariate Gaussian mixture distributions. This approach can naturally capture the interactions between adjacent buses (e.g., correlated speed and smooth variation of headway), handle missing values in data, and depict the multimodality in bus travel time distributions. Next, we assume different periods in a day share the same set of Gaussian components but different mixing coefficients to characterize the systematic temporal variations in bus operation. For model inference, we develop an efficient Markov chain Monte Carlo (MCMC) sampling algorithm to obtain the posterior distributions of model parameters and make probabilistic forecasting. We test the proposed model using the data from a twenty-link bus route in Guangzhou, China. Results show our approach significantly outperforms baseline models that overlook bus-to-bus interactions in terms of both predictive means and distributions. Besides forecasting, the parameters of the proposed model contain rich information for understanding/improving the bus service.

Understanding the long-term impact that changes in a city's transportation infrastructure have on its spatial interactions remains a challenge. The difficulty arises from the fact that the real impact may not be revealed in static or aggregated mobility measures, as these are remarkably robust to perturbations. More generally, the lack of longitudinal, cross-sectional data demonstrating the evolution of spatial interactions at a meaningful urban scale also hinders us from evaluating the sensitivity of movement indicators, limiting our capacity to understand the evolution of urban mobility in depth. Using very large mobility records distributed over three years we quantify the impact of the completion of a metro line extension: the circle line (CCL) in Singapore. We find that the commonly used movement indicators are almost identical before and after the project was completed. However, in comparing the temporal community structure across years, we do observe significant differences in the spatial reorganization of the affected geographical areas. The completion of CCL enables travelers to re-identify their desired destinations collectively with lower transport cost, making the community structure more consistent. These changes in locality are dynamic, and characterized over short time-scales, offering us a different approach to identify and analyze the long-term impact of new infrastructures on cities and their evolution dynamics., Comment: 8 pages, 4 figures; J. R. Soc. Interface 20141089