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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. 

Drivers traveling on the road usually choose the route which will reduce their own travel time without giving a thought about how this decision will affect other users in the traffic network. Their behaviours leads to problem of oscillating congestion on the roads in the event of traffic disruption. This paper addresses this issue by adopting a competing optimal approach for informed and uninformed drivers. Informed drivers are proposed with alternate routes that reduce the system cost while uninformed drivers continue their journey on originally proposed routes. This strategy of dispersing traffic can reduce congestion significantly. The framework is implemented using Transmodeler, a traffic simulation by experimenting with varying percentage of informed drivers in the network. 

Estimating multimodal distributions of travel times 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 prediction model is developed that shares observations across similarly distributed network segments across 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. Compared to traditional prediction without those updates, the proposed model's 19% of performance show the benefit of indirect learning. Different from traditional travel time prediction tools, the developed model can be used by traffic and planning agencies in knowing how far back in history and what sample size of historic data would be useful for current prediction. 

We introduce temporal multimodal multivariate learning, a new family of decision making models that can indirectly learn and transfer online information from simultaneous observations of a probability distribution with more than one peak or more than one outcome variable from one time stage to another. We approximate the posterior by sequentially removing additional uncertainties across different variables and time, based on data-physics driven correlation, to address a broader class of challenging time-dependent decision-making problems under uncertainty. Extensive experiments on real-world datasets ( i.e., urban traffic data and hurricane ensemble forecasting data) demonstrate the superior performance of the proposed targeted decision-making over the state-of-the-art baseline prediction methods across various settings. 

While there has been significant progress on statistical theories in the information community, there is a lack of studies in information-theoretic distributed resource allocation to maximize information gain. With advanced technologies of unmanned aerial vehicles (UAVs) in response to corresponding revised FAA regulations, this study focuses on developing a new framework for utilizing UAVs in incident management. As a result of new computing technologies, predictive decision-making studies have recently improved ERV allocations for a sequence of incidents; however, these ground-based operations do not simultaneously capture network-wide information. This study incorporates a real-time aerial view using UAVs with three key improvements. First, aerial observations update the status of the freeway shoulder, allowing an ERV to safely travel at full speed. Second, observing parameters of the congestion shockwave provides accurate measurements of the true impact of an incident. Third, real-time information can be gathered on the clearance progress of an incident scene. We automate UAV and ERV allocation while satisfying constraints between these vehicles using a distributed constraint optimization problem (DCOP) framework. To find the optimal assignment of vehicles, the proposed model is formulated and solved using the Max-Sum approach. The system utility convergence is presented for different scenarios of grid size, number of incidents, and number of vehicles. We also present the solution of our model using the Distributed Stochastic Algorithm (DSA). DSA with exploration heuristics outperformed the Max-Sum algorithm when probability threshold p=0.5 but degrades for higher values of p.