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Traffic shockwaves demonstrate the formation and spreading of traffic fluctuation on roads. Existing methods mainly detect the shockwaves and their propagation by estimating traffic density and flow, which presents weaknesses in applications when traffic data is only partially or locally collected. This paper proposed a four-step data-driven approach that integrates machine learning with the traffic features to detect shockwaves and estimate their propagation speeds only using partial vehicle trajectory data. Specifically, we first denoise the speed data derived from trajectory data by the Fast Fourier Transform (FFT) to mitigate the effect of spontaneous random speed fluctuation. Next, we identify trajectory curves’ turning points where a vehicle runs into a shockwave and its speed presents a high standard deviation within a short interval. Furthermore, the Density-based Spatial Clustering of Applications with Noise algorithm (DBSCAN) combined with traffic flow features is adopted to split the turning points into different clusters, each corresponding to a shockwave with constant speed. Last, the one-norm distance regression method is used to estimate the propagation speed of detected shockwaves. The proposed framework was applied to the field data collected from the I-80 and US-101 freeway by the Next Generation Simulation (NGSIM) program. The results show that this four-step data-driven method could efficiently detect the shockwaves and their propagation speeds without estimating the traffic densities and flows nearby. It performs well for both homogenous and nonhomogeneous road segments with trajectory data collected from total or partial traffic flow. 

This paper studies sample average approximation (SAA) and its simple regularized variation in solving convex or strongly convex stochastic programming problems. Under heavy-tailed assumptions and comparable regularity conditions as in the typical SAA literature, we show — perhaps for the first time — that the sample complexity can be completely free from any complexity measure (e.g., logarithm of the covering number) of the feasible region. As a result, our new bounds can be more advantageous than the state-of-the-art in terms of the dependence on the problem dimensionality.