Bayesian Dynamic Gamma Models for Route-Level Travel Time Reliability

2026-02-06

AI Summary

Existing approaches to modeling path travel time struggle to balance accuracy and computational efficiency: models relying on independence assumptions suffer from poor calibration, while complex simulation-based methods incur prohibitive computational costs. This work proposes a conjugate Bayesian dynamic Gamma model that captures inter-segment dependencies through a shared latent environmental process, preserving conditional independence for tractable inference. By leveraging moment-matching approximation, the method yields a closed-form F-distribution for path travel time with O(1) computational complexity—the first such result to our knowledge. Evaluated on an 8.26-mile segment of Chicago’s I-55 freeway, the approach achieves a 95.4% empirical coverage rate within its 90% prediction intervals, substantially outperforming independent models (34–37%) at comparable computational cost, thereby overcoming the longstanding trade-off between precision and efficiency.

Technology Category

Planning, Routing, and Scheduling: Model-Based ReasoningReasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Bayesian Learning

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalizationSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Route-level travel time reliability requires characterizing the distribution of total travel time across correlated segments -- a problem where existing methods either assume independence (fast but miscalibrated) or model dependence via copulas and simulation (accurate but expensive). We propose a conjugate Bayesian dynamic Gamma model with a common random environment that resolves this trade-off. Each segment's travel time follows a Gamma distribution conditional on a shared latent environment process that evolves as a Markov chain, inducing cross-segment dependence while preserving conditional independence. A moment-matching approximation yields a closed-form $F$-distribution for route travel time, from which the Planning Time Index, Buffer Index, and on-time probability are computed instantly -- at the same $O(1)$ cost as independence-based methods. The conjugate structure ensures that Bayesian posterior updates and the full predictive distribution are available in closed form as new sensor data arrives. Applied to 16 sensors spanning 8.26 miles on I-55 in Chicago, the model achieves 95.4% coverage of nominal 90\% predictive intervals versus 34--37% for independence-based convolution, at identical computational cost.

Problem

• travel time reliability
• route-level modeling
• cross-segment dependence
• predictive distribution
• Bayesian inference

Innovation

• Bayesian dynamic model
• travel time reliability
• Gamma distribution
• shared random environment
• closed-form inference