Bayesian Dynamic Gamma Models for Route-Level Travel Time Reliability

TL;DR

This paper introduces a Bayesian dynamic Gamma model for route travel time reliability that captures dependence across segments efficiently, providing accurate predictive intervals with minimal computational cost.

Contribution

It proposes a conjugate Bayesian dynamic Gamma model with a shared latent environment to model correlated travel times, enabling fast, accurate, and closed-form predictive distributions.

Findings

Achieves 95.4% coverage of 90% predictive intervals on real data.

Outperforms independence-based methods in coverage while maintaining same computational cost.

Provides closed-form Bayesian updates and predictions for travel time reliability.

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.