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High level architecture (HLA) is a well-known standard for constructing and supporting large-scale and complex distributed interactive simulation systems. HLA has several key components, among which; run-time infrastructure (RTI) is a crucial one as a service provider engine in HLA based simulation systems. Real Time extension of HLA/RTI became very important due to the necessity for the HLA to support simulation components with strict time constraints while interacting with each other. In fact, there have been a lot of research and concerns with regard to designing a high performance RT-RTI. In this paper, we propose a novel RT-RTI design approach that uses Real Time Discrete Event System Specification (RT-DEVS) formalism to model and simulate vital experimental frames. We are presenting a case study that demonstrates the usefulness of this formal approach in predicting the key design characteristics through designated simulation experiments. The simulation experimental results show that dynamic thread pool management with our load balancing strategies formed a key in improving the performance of RT-RTI in terms of serving tasks within their deadlines. Through our proposed formal design approach, we have seen an open area in finding the optimal RT-RTI design using RT-DEVS.