Internet of Things (IoT) applications consist of diverse Things (sensors and devices) in terms of hardware resources. Furthermore, such applications are characterized by the Things' mobility and multiple interaction types, such as synchronous, asynchronous, and streaming. Middleware IoT protocols consider the above limitations and support the development of effective applications by providing several Quality of Service features. These features aim to enable application developers to tune an application by switching different levels of response times and delivery success rates. However, the profusion of the developed IoT protocols and the intermittent connectivity of mobile Things, result to a non-trivial application tuning. In this paper, we model the performance of the middleware overlay infrastructure using Queueing Network Models. To represent the mobile Thing's connections/disconnections, we model and solve analytically an ON/OFF queueing center. We apply our approach to Streaming interactions with mobile peers. Finally, we validate our model using simulations. The deviations between the performance results foreseen by the analytical model and the ones provided by the simulator are shown to be less than 5%.