Real-time (RT) systems include hardware and software components interacting in a tight fashion. Although formal methods for RT systems development have advanced, they are sometimes difficult to apply in practical applications, and scalability is compromised as the complexity of the system scales up. Instead, using modeling and simulation (M&S) methods and tools has showed to be useful for verification of practical aspects of RT systems (and having the advantage to be able to including models of the physical environment they interact with). Although several efforts exist in M&S of RT systems, none of them has considered problems of transient overloading in the RT systems specifications. Here, we introduce a new theoretical framework called I-DEVS (imprecise discrete event systems specification) with the goal of guaranteeing responses to inputs within specified time constraints under such transient overloading conditions. The solution presented here has the advantages of a formal specification and the practicality of an M&S-based approach. We also discuss how to define hierarchical models running in RT, and we present a set of tools that can be applied to develop RT-embedded applications, and RT simulations.