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Estimating multimodal distributions of travel times (TT) from real-world data is critical for understanding and managing congestion. Mixture models can estimate the overall distribution when distinct peaks exist in the probability density function, but no transfer of mixture information under epistemic uncertainty across different spatiotemporal scales has been considered for capturing unobserved heterogeneity. In this paper, a physics-informed and -regularized (PIR) prediction model is developed that shares observations across similarly distributed network segments over time and space. By grouping similar mixture models, the model uses a particular sample distribution at distant non-contiguous unexplored locations and improves TT prediction. The model includes hierarchical Kalman filtering (KF) updates using the traffic fundamental diagram to regulate any spurious correlation and estimates the mixture of TT distributions from observations at the current location and time sampled from the multimodal and multivariate TT distributions at other locations and times. In order to overcome the limitations of KF, this study developed dynamic graph neural network (GCN) model which uses time evolving spatial correlations. The KF model with PIR predicts traffic state with 19% more accuracy than TMML model in Park et al.(2022) and GCN model will further reduce the uncertainty in prediction. This study uses information gain from explored correlated links to obtain accurate predictions for unexplored ones. 

Traffic systems exhibit supply-side uncertainty which is alleviated through real-time information. This article explores subscription models for a private agency sharing data at a fixed rate. A multiclass strategy-based equilibrium model is developed for two classes of subscribed and unsubscribed travelers, whose optimal strategy given the link-state costs is modeled as a Markov decision process (MDP) and a partially-observable MDP, respectively. A utility-based subscription choice model is formulated to study the impacts of subscription rates on the percentage of travelers choosing to subscribe. Solutions to the fixed-point formulation are determined using iterative algorithms. The proposed subscription model can be used for designing optimal subscription rates in various settings where real-time information can be a valuable routing tool such as express lanes, parking systems, roadside delivery, and routing of vulnerable road users. 

Traffic systems exhibit supply-side uncertainty which is alleviated through real-time information. This article explores subscription models for a private agency sharing data at a fixed rate. A multiclass strategy-based equilibrium model is developed for two classes of subscribed and unsubscribed travelers, whose optimal strategy given the link-state costs is modeled as a Markov decision process (MDP) and a partially-observable MDP, respectively. A utility-based subscription choice model is formulated to study the impacts of subscription rates on the percentage of travelers choosing to subscribe. Solutions to the fixed-point formulation are determined using iterative algorithms. The proposed subscription model can be used for designing optimal subscription rates in various settings where real-time information can be a valuable routing tool such as express lanes, parking systems, roadside delivery, and routing of vulnerable road users.