Numerous middleware application programming interfaces (APIs) and protocols were introduced in the literature in order to facilitate the application development of the Internet of Things (IoT). Such applications are built on reliable or even unreliable protocols that may implement different quality-of-service (QoS) delivery modes. The exploitation of these protocols, APIs and QoS modes, can satisfy QoS requirements in critical IoT applications (e.g., emergency response operations). To study QoS in IoT applications, it is essential to leverage a performance analysis methodology. Queueing-network models offer a modeling and analysis framework that can be adopted for the IoT interactions of QoS representation through either analytical or simulation models. In this paper, various types of queueing models are presented that can be used for the representation of various QoS settings of IoT interactions. In particular, we propose queueing models to represent message-drop probabilities, intermittent mobile connectivity, message availability or validity, the prioritization of important information, and the processing or transmission of messages. Our simulation models demonstrate the significant effect on delivery success rates and response times when QoS settings are varied.