Traffic forecasting is a classical task for traffic management and it plays an important role in intelligent transportation systems. However, since traffic data are mostly collected by traffic sensors or probe vehicles, sensor failures and the lack of probe vehicles will inevitably result in missing values in the collected raw data for some specific links in the traffic network. Although missing values can be imputed, existing data imputation methods normally need long-term historical traffic state data. As for short-term traffic forecasting, especially under edge computing and online prediction scenarios, traffic forecasting models with the capability of handling missing values are needed. In this study, we consider the traffic network as a graph and define the transition between network-wide traffic states at consecutive time steps as a graph Markov process. In this way, missing traffic states can be inferred step by step and the spatial-temporal relationships among the roadway links can be Incorporated. Based on the graph Markov process, we propose a new neural network architecture for spatial-temporal data forecasting, i.e. the graph Markov network (GMN). By incorporating the spectral graph convolution operation, we also propose a spectral graph Markov network (SGMN). The proposed models are compared with baseline models and tested on three real-world traffic state datasets with various missing rates. Experimental results show that the proposed GMN and SGMN can achieve superior prediction performance in terms of both accuracy and efficiency. Besides, the proposed models parameters, weights, and predicted results are comprehensively analyzed and visualized.
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