A Bayesian Markov mesh regime-switching regression model for bus travel time forecasting

Probabilistic forecasting of bus travel time is crucial for enhancing the reliability and efficiency of public transportation. Traditional deterministic models often neglect the inherent uncertainties in travel time forecasts. While there are a few studies on probabilistic forecasting for bus travel time, they either lack interpretability or inadequately capture the complex dynamics of bus operation. To address the gaps, this paper develops the Bayesian Markov Mesh regime-switching regression model to probabilistically forecast bus travel time. This novel model extends the conventional one-dimensional hidden Markov regime-switching regression model with a two-dimensional mesh structure, which can capture dynamics in both link-to-link and bus-to-bus dimensions. Moreover, this model can capture the multimodal and skewed nature of bus travel time distributions. For model inference, we develop an efficient Markov chain Monte Carlo (MCMC) algorithm to obtain the posterior distributions of model parameters and make probabilistic forecasting for bus travel time. Empirical evaluations with real-world data demonstrate the superiority of our approach over baseline models in both predictive means and distributions. Furthermore, our model offers insights into the dynamic propagation of link travel times, presenting potential implications for understanding and optimizing bus systems.