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Traffic problems have seriously affected people's life quality and urban development, and forecasting the short-term traffic congestion is of great importance to both individuals and governments. However, understanding and modeling the traffic conditions can be extremely difficult, and our observations from real traffic data reveal that (1) similar traffic congestion patterns exist in the neighboring time slots and on consecutive workdays; (2) the levels of traffic congestion have clear multiscale properties. To capture these characteristics, we propose a novel method named PCNN based on deep Convolutional Neural Network, modeling Periodic traffic data for short-term traffic congestion prediction. PCNN has two pivotal procedures: time series folding and multi-grained learning. It first temporally folds the time series and constructs a two-dimensional matrix as the network input, such that both the real-time traffic conditions and past traffic patterns are well considered; then with a series of convolutions over the input matrix, it is able to model the local temporal dependency and multiscale traffic patterns. In particular, the global trend of congestion can be addressed at the macroscale; whereas more details and variations of the congestion can be captured at the microscale. Experimental results on a real-world urban traffic dataset confirm that folding time series data into a two-dimensional matrix is effective and PCNN outperforms the baselines significantly for the task of short-term congestion prediction.