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Cellular networks have been widely deployed and are under ever-growing pressure from increasing energy consumption. Identifying the spatio-temporal properties of network traffic is crucial to effectively manage large-scale cellular networks and to optimize energy control strategies. However, traditional methods need to construct complex mathematical models to describe the properties of traffic, making the process inefficient and not automatic. Recent methods based on deep learning techniques are unexplainable and untraceable. In this paper, we propose a novel modeling and analysis approach by applying the spatio-temporal model checking technique to the identification of network traffic properties. First, we model the spatial structure of the cellular network by a closure space and the temporal structure of network traffic by the Kripke structure. Second, we provide logical characterizations of the spatio-temporal properties of network traffic by suitable spatio-temporal logic of closure space (STLCS) formulas. Third, we use model checking algorithms to detect the spatio-temporal properties of network traffic and to visualize the results. The experiments are illustrated with the Milan network traffic dataset and indicate that our approach can automatically and effectively detect desirable spatio-temporal properties of cellular network traffic. [ABSTRACT FROM AUTHOR]