Discrete-event (DE) models are formal system specifications that have analyzable deterministic behaviors. Using a global, consistent notion of time, DE components communicate via time-stamped events. DE models have primarily been used in performance modeling and simulation, where time stamps are a modeling property bearing no relationship to real time during execution of the model. In this paper, we extend DE models with the capability of relating certain events to physical time. We propose a programming model, called PTIDES (Programming Temporally Integrated Distributed Embedded Systems), which has DE semantics, but with carefully chosen relations between model time and real time. Key to making this model effective is to ensure that constraints that guarantee determinacy in the semantics are preserved at runtime. To accomplish this, we give a distributed execution strategy that obeys DE semantics without the penalty of totally ordered executions based on time stamps. Our technique relies on having a distributed common notion of time, known to some precision. Based on causality analysis of DE models, we define relevant dependency and relevant orders to enable out-of-order execution without compromising determinism and without requiring backtracking.