Traffic sensors do not provide a perfect record. Some readings vanish at random, and a broken detector may leave a whole stretch of time blank. Filling those gaps matters because a missing value can distort both the picture of past congestion and the models trained to forecast it.
Missing readings appear as holes in an array organized by road, day, and time. Many days share similar rhythms, and neighboring roads often experience related changes. A Bayesian tensor model uses those recurring structures to infer the absent values while also expressing uncertainty about them. The restored matrix at the end is the visual payoff: information from the rest of the system can recover a plausible traffic history where no direct measurement exists. This is reconstruction under uncertainty, not a claim that the lost readings can be known with perfect accuracy.
Large language models can generate many plausible travel choices, but plausible is not the same as representative of real travelers. In the same choice situation, a human sample and an artificial sample may favor different options. If those differences are ignored, adding more synthetic responses can make a demand model more confident about the wrong behavior.
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Crashes are infrequent, yet road agencies must decide where to investigate or intervene before the next one occurs. That creates a prediction problem: can the conditions of a road segment help estimate its future crash count? Traffic volume, geometry, and other recorded features may interact in ways a simple straight-line rule misses.
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A road does not evolve in isolation. Speed on one link can be affected by traffic arriving from upstream, queues spilling back from downstream, and conditions on neighboring links. Forecasting several steps ahead therefore requires more than extending each road's own recent trend.
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