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The current industry trend is to replace the use of custom components with standards-based Commercially available Off-The-Shelf (COTS) based hardware and protocols. Furthermore, the emergence of new industrial paradigms, such as Industry 4.0 and the Industrial Internet of Things, sets additional requirements regarding e.g. scale, transparency, agility, flexibility and efficiency. Therefore, in these domains, application layer protocols such as Message Queuing Telemetry Transport protocol (MQTT) are gaining popularity, in result of their simplicity, scalability, low resource-usage and decoupling between end nodes. However, such protocols were not designed for real-time applications, missing key features such as determinism and latency bounds. A recent work proposed extending MQTT with real-time services, taking advantage of Software Defined Networking (SDN) to manage the network resource. These extensions allow applications to specify real-time requirements that are then captured by a resource manager and used to reserve the necessary resources at the network layer. This paper shows that such MQTT extended architecture is analyzable from a worst-case timing perspective. We derive a system model that captures the real-time features and we present a response-time analysis to assess the schedulability of the real-time traffic. Finally, we validate the analysis with a set of experimental results.