We now use the Internet of things (IoT) in our everyday lives. The novel IoT devices collect cyber–physical data and provide information on the environment. Hence, IoT traffic will count for a major part of Internet traffic; however, its impact on the network is still widely unknown. IoT devices are prone to cyberattacks because of constrained resources or misconfigurations. It is essential to characterize IoT traffic and identify each device to monitor the IoT network and discriminate among legitimate and anomalous IoT traffic. In this study, we deployed a smart-home testbed comprising several IoT devices to study IoT traffic. We performed extensive measurement experiments using a novel IoT traffic generator tool called IoTTGen. This tool can generate traffic from multiple devices, emulating large-scale scenarios with different devices under different network conditions. We analyzed the IoT traffic properties by computing the entropy value of traffic parameters and visually observing the traffic on behavior shape graphs. We propose a new method for identifying traffic entropy-based devices, computing the entropy values of traffic features. The method relies on machine learning to classify the traffic. The proposed method succeeded in identifying devices with a performance accuracy up to 94% and is robust with unpredictable network behavior with traffic anomalies spreading in the network.