Probabilistic Prediction of Bus Headway Using Relevance Vector Machine Regression

Bus headway regularity heavily affects transit riders' attitude for choosing public transportation and also serves as an important indicator for transit performance evaluation. Therefore, an accurate estimate of bus headway can benefit both transit riders and transit operators. This paper proposed a relevance vector machine (RVM) algorithm to predict bus headway by incorporating the time series of bus headways, travel time, and passenger demand at previous stops. Different from traditional computational intelligence approaches, RVM can output the probabilistic prediction result, in which the upper and lower bounds of a predicted headway within a certain probability are yielded. An empirical experiment with two bus routes in Beijing, China, is utilized to confirm the high precision and strong robustness of the proposed model. Five algorithms [support vector machine (SVM), genetic algorithm SVM, Kalman filter, k-nearest neighbor, and artificial neural network] are used for comparison with the RVM model and the result indicates that RVM outperforms these algorithms in terms of accuracy and confidence intervals. When the confidence level is set to 95%, more than 95% of actual bus headways fall within the prediction bands. With the probabilistic bus headway prediction information, transit riders can better schedule their trips to avoid late and early arrivals at bus stops, while transit operators can adopt the targeted correction actions to maintain regular headway for bus bunching prevention.