In this paper, we propose a methodology for producing correct-by-construction Time-Triggered (TT) physical model by starting from a high-level model of the application software in Behaviour, Interaction, Priority (BIP). BIP is a component-based framework with formal semantics that rely on multi-party interactions for synchronizing components. Commonly in TT implementations, processes interact with each other through a communication medium. Our methodology transforms, depending on a user-defined task mapping, high-level BIP models where communication between components is strongly synchronized, into TT physical model that integrates a communication medium. Thus, only inter-task communications and components participating in such interactions are concerned by the transformation process. The transformation consists of: (1) breaking atomicity of actions in components by replacing strong synchronizations with asynchronous send/receive interactions, (2) inserting communication media that coordinate execution of inter-task interactions according to a user-defined task mapping, (3) extending the model with an algorithm for handling conflicts between different communication media and (4) instantiating task components and adding local priority rules for handling conflicts between inter-task and intra-task interactions. We also prove the correctness of our transformation, which preserves safety properties. I. INTRODUCTION A Time-Triggered (TT) system initiates all system activities-task activation, message transmission, and message detection-at predetermined points in time. Ideally, in a time-triggered operating system there is only one interrupt signal: the ticks generated by the local periodic clock. These statically defined activation instants enforce regularity and make TT systems more predictable than Event-Triggered (ET) systems. This approach is well-suited for hard real-time systems. In [1] and [2], Kopetz presents an approach for real-time system design based on the TT paradigm which comprises three essential elements: The global notion of time: It must be established by a periodic clock synchronization in order to enable a TT communication and computation, The temporal control structure of each task: In a sequence of computational or communication processes (called tasks), the start of a task is triggered by the progression of the global time, independently from the involved data of the task. The worst-case execution time and thus the worst-case termination instant are also assumed to be known a priori. These statically predefined start and worst-case termination instants, define the temporal control structure of the task,