Anomaly detection in video surveillance has recently gained interest from the research community. Temporal duration of anomalies vary within video streams, leading to complications in learning the temporal dynamics of specific events. This paper presents a temporal-granularity method for an anomaly detection model (TeG) in real-world surveillance, combining spatio-temporal features at different time-scales. The TeG model employs multi-head cross-attention blocks and multi-head self-attention blocks for this purpose. Additionally, we extend the UCF-Crime dataset with new anomaly types relevant to Smart City research project. The TeG model is deployed and validated in a city surveillance system, achieving successful real-time results in industrial settings.