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Traffic flow forecasting (TFF) is critical for constructing intelligent transportation systems and offering real-time traffic applications, and especially accurate flow forecasting based on traffic big data can drive reliable strategies for traffic management and control. To consider the weight of the influence of the spatial correlation among the road segments and capture the nonlinear characteristics of traffic flow, this paper presents a parallel Normal Distribution and Attention Mechanism Weighted Deep Bidirectional Long Short-Term Memory (NAW-DBLSTM) algorithm on Spark. Specifically, we employ the resilient distributed data set (RDD) to preprocess large-scale mobile trajectory data (e.g., taxi GPS trajectory data), and then Kalman Filter (KF) is utilized to smooth the taxi trajectory big data. Next, the parallel NAW-DBLSTM algorithm is put forward on a Spark distributed computing platform to enhance the accuracy and scalability of TFF, combined with the attention mechanism and the normal distribution, and then the time window is used for TFF. Finally, the traffic flow is forecasted successfully on Spark by our NAW-DBLSTM algorithm with the real-world GPS trajectories of taxicabs. The experimental results demonstrate that, compared with LSTM, BiLSTM, DBLSTM, DNN, SVR, KNN, SAEs, BP, CNN, GRU, and ANNs, NAW-DBLSTM can produce better performance with the MAPE value that is 85.1%, 80.1%, 85.8%, 73.1%, 78.2%, 77.9%, 78.8%, 84.6%, 96.4%, 86.2%, and 73.2% lower than that of comparable algorithms, respectively. Particularly, the MAPE value of NAW-DBLSTM is 28.3%, 20.1%, 71.1%, and 79.1% lower than that of LSTM weighted with the normal distribution and the attention mechanism (NAW-LSTM), BiLSTM weighted with the normal distribution and the attention mechanism (NAW-BiLSTM), DBLSTM weighted with the normal distribution (NW-DBLSTM), and NAW-DBLSTM weighted without the time window (NT-NAW-DBLSTM), respectively. [ABSTRACT FROM AUTHOR]