Devices and systems used in distributed environments, such as on trains or in power plants, should be able to respond to external changes in real-time. Real-time middleware such as one based on the TMO (Time-Triggered Message-Triggered Object) model is considered recently as a choice to adapt real-time properties to distributed systems. TMO middleware guarantees that systems in distributed environments operate in a reliable manner. This middleware does not have an adequate monitoring infrastructure or supporting tools used in distributed environments, however. As such, this paper proposes TSDS (TMO-based Sharing and Delivery Scheme) as a part of the monitoring infrastructure. This is configured within the TMO middleware to share and deliver monitoring data among TMO-based real-time systems. The results of experiments show that the TSDS instrumentation overhead is less than 1ms. This means that TSDS has little effect on the operation of the middleware.