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System-level decision making in transportation needs to understand day-to-dayvariation of network flows, which calls for accurate modeling and estimation ofprobabilistic dynamic travel demand on networks. Most existing studies estimatedeterministic dynamic origin-destination (OD) demand, while the day-to-dayvariation of demand and flow is overlooked. Estimating probabilisticdistributions of dynamic OD demand is challenging due to the complexity of thespatio-temporal networks and the computational intensity of thehigh-dimensional problems. With the availability of massive traffic data andthe emergence of advanced computational methods, this paper develops adata-driven framework that solves the probabilistic dynamic origin-destinationdemand estimation (PDODE) problem using multi-day data. Different statisticaldistances (e.g., lp-norm, Wasserstein distance, KL divergence, Bhattacharyyadistance) are used and compared to measure the gap between the estimated andthe observed traffic conditions, and it is found that 2-Wasserstein distanceachieves a balanced accuracy in estimating both mean and standard deviation.The proposed framework is cast into the computational graph and areparametrization trick is developed to estimate the mean and standarddeviation of the probabilistic dynamic OD demand simultaneously. We demonstratethe effectiveness and efficiency of the proposed PDODE framework on both smalland real-world networks. In particular, it is demonstrated that the proposedPDODE framework can mitigate the overfitting issues by considering the demandvariation. Overall, the developed PDODE framework provides a practical tool forpublic agencies to understand the sources of demand stochasticity, evaluateday-to-day variation of network flow, and make reliable decisions forintelligent transportation systems.

Estimating probabilistic dynamic origin-destination demands using multi-day traffic data on computational graphs