The Internet of Things (IoT) is a concept that connects things and objects from the environment and everyday life into a global network and serves as a foundation for development of advanced, self-configuring services adapted to the user context. The thesis presents the CUPUS middleware, an open-source publish/subscribe solution for IoT environment. The CUPUS middleware is compared with other publish/subscribe solutions, and the thesis provides classification of publish/subscribe solutions reported in the literature in seven groups based on their capabilities and characteristics. The thesis proposes analytical modelling of aggregate input load of IoT services and modelling of processing times of publish/subscribe components using well-known distributions. Finally, a process to create a Queueing Theory model of publish/subscribe solution is proposed and demonstrated on the CUPUS middleware. The output of the model that estimates the processing time at individual component or in the system overall is in accordance with the results that were collected during the experimental evaluation of the middleware. The scientific contribution of the proposed research in the doctoral thesis is the following: - a taxonomy of cloud-based publish/subscribe systems for continuous processing of sensor data streams in the area of the IoT; - analytical performance model of cloud-based publish/subscribe systems based on queueing theory; - verification method of the analytical performance model which compares modelling results with the observed publish/subscribe system.