As we consider the number of IoT time-sensitive applications , the transfer of data to a remote data center and server such as Cloud, Fog, and Edge becomes inefficient since the deadline constraint is not satisfied. Thus, ensuring that the IoT time-sensitive applications meet their timing constraints is a challenge. Mist Computing is closer to IoT devices, presenting the lowest communication delay but less computational resource than the Cloud, Fog, and Edge. Seeing several IoT devices use MQTT protocol to access the data due to its lightness and flexibility, we propose an architecture for IoT time-sensitive applications based on MQTT protocol and integrating Mist Computing. We focus on distributing the MQTT brokers over Mist nodes to satisfy the deadline constraints with the consideration of the limited resource of Mist nodes. Hence, we propose an approach for the selection of the appropriate MQTT Mist broker. We have also proposed MQTT communication model that provides the M/M/1 based analysis for delay computing and energy conception. The experiment results show that our proposal is very effective for time-sensitive applications and also maximize the lifetime of IoT systems since it minimizes the cumulative energy of the system. Compared to MQTT Edge broker distribution, our solution provides the lesser delay of communication between IoT devices.