Joint State Estimation of Real-Time Transit Travel Time and Reliability Bounds

Uncertainty in bus travel times because of congestion, signal delays, dwell times, and data gaps poses significant challenges for passengers and operators. Existing real-time information systems primarily disseminate point estimates of arrival times, which fail to convey uncertainty, undermining passenger trust and complicating operational planning. This study develops a hazard-based framework for the joint real-time estimation of bus travel time and its reliability bounds to address these limitations. The approach leverages accelerated failure time (AFT) models to dynamically update mean and variability estimates while handling censored observations from incomplete Global Positioning System bus trajectories. Among alternative parametric forms evaluated using multi-criteria performance metrics and the technique for order preference by similarity to ideal solution (TOPSIS) ranking method, the log-normal AFT model applied to pace (travel time per unit distance) delivers the most reliable predictions, achieving near-nominal coverage, narrower intervals, and interpretable hazard structures aligned with real-world transit dynamics. Comparative analysis against alternative regression benchmarks confirmed that ignoring the dependence between mean and variability leads to biased reliability estimates. Empirical insights highlight pronounced spatial and temporal heterogeneity, with congestion during peak hours and route-specific factors significantly shaping uncertainty. Sensitivity analysis underscored the operational significance of reliability management: a 30% reduction in median travel time produced ∼21% improvements in both mean travel time (∼17 min) and reliability interval width (∼9 min). In comparison, a 30% reduction in variability lowered interval width by ∼9% (∼4 min). These findings establish the hazard-based framework as a robust, interpretable basis for delivering reliability-aware traveler information and supporting data-driven operational strategies in heterogeneous urban transit environments.