Bus travel time prediction: a log-normal auto-regressive (AR) modelling approach

Abstract

Providing real-time arrival time information of the transit buses has become inevitable in urban areas to improve the efficiency of the public transportation system. However, accurate prediction of arrival time of buses is still a challenging problem in dynamically varying traffic conditions especially under heterogeneous traffic condition without lane discipline. One broad approach researchers have adopted over the years is to divide the entire bus route into sections and model the correlations of section travel times either spatially or temporally. The proposed study adopts this approach of working with section travel times and developed two predictive modelling methodologies namely (a) classical time-series approach employing a seasonal AR model with possible integrating non-stationary effects and (b) linear non-stationary AR approach, a novel technique to exploit the notion of partial correlation for learning from data to exploit the temporal correlations in the bus travel time data. Many of the reported studies did not explore the distribution of travel time data and incorporated their effects into the modelling process while implementing time series approach. The present study conducted a detailed analysis of the marginal distributions of the data from Indian conditions (that we use for testing in this paper). This revealed a predominantly log-normal behaviour which was incorporated into the above proposed predictive models. Towards a complete solution, the study also proposes a multi-section ahead travel time prediction algorithm based on the above proposed classes of temporal models learnt at each section to facilitate real time implementation. Finally, the predicted travel time values were corroborated with the actual travel time values. From the results, it was found that the proposed method was able to perform better than historical average, exponential smoothing, ARIMA, and ANN methods and the methods that considered either temporal or spatial variations alone.

Traffic congestion prediction based on Estimated Time of Arrival

“…The authors did not apply multiple classifiers as a comparison and statistical analysis of the dataset is not available. B. Dhivya Bharathi et al [ 15 ] have proposed the sequential non-stationary model for predicting the bus arrival time under heterogeneous traffic conditions. They have worked on time series dataset of buses containing total 1231 trips spanning across 34 days.…”

Bus Single-Trip Time Prediction Based on Ensemble Learning

“…Bie et al [ 25 ] performed bus single-trip time prediction based on bus GPS data, but the model built did not consider the real-time status of traffic flow and roads. Dhivya Bharathi et al [ 26 ] used the historical data averaging method and TS method for predicting the transit section running time but lacked influencing factors. Chang et al [ 27 ] predicted the bus single-trip time using a regression algorithm based on historical data well, but the predictive model is quite complicated.…”

BusTr

“…Dhivyabharathi et al [8] use real-time bus location information as a proxy for tra c with the aim of predicting BusTr travel times over each segment of a trip. ey note that their data has a log-normal distribution and build two predictors around this: a seasonal AR model with possibly non-stationary e ects and a linear non-stationary AR model.…”

“…is allows us to avoid having to incorporate strong priors such as log-normality [8]. (d) Our model makes inferences from real-time tra c data.…”