Discrete-event (DE) models are formal system specifications that have analyzable deterministic behaviors in terms of event values and time stamps. However, since time is only a modeling property, they are primarily used in performance modeling and simulation. In this paper, we extend discrete-event models with the capability of mapping certain events to physical time and propose them as a programming model, called PTIDES. We seek analysis tools and execution strategies that can preserve the deterministic behaviors specified in DE models without paying the penalty of totally ordered executions. This is particularly intriguing in time synchronized distributed systems since there is a consistent global notion of time and intrinsic parallelism among the nodes. Based on causality analysis of DE systems, we define relevant dependency and relevant orders to enable outof- order executions without hurting determinism and without requiring backtracking. For a given network characteristic, we can check statically whether deploying the model in the network can preserve the real-time properties in the specification.