Bayesian inference for link travel time correlation of a bus route

Abstract

Estimation of link travel time correlation of a bus route is essential to many bus operation applications. Link travel time on a bus route could exhibit complex correlation structures, such as long-range correlations, negative correlations, and time-varying correlations. This paper develops a Bayesian Gaussian model to estimate the link travel time correlation matrix of a bus route using smart-card-like data. Our method overcomes the small-sample-size problem in correlation matrix estimation by borrowing/integrating those incomplete observations from other bus routes. We first conduct a synthetic experiment and results show that the proposed method produces an accurate estimation for correlations with credible intervals. Next, we perform experiments on a real-world bus route with in-out-stop record data; results show that both local and long-range correlations exist on this bus route. Finally, we demonstrate an application of using the estimated covariance matrix to make probabilistic forecasting of link and trip travel time.