The paper shows how a recently introduced class of applications can be solved by constraint programming. This new type of application is due to the emergence of special real-time systems, enjoying increasing popularity in such diverse areas as automotive electronics and aerospace industry. These real-time systems are time triggered in the sense that their overall behavior is globally controlled by a recurring clock tick. For this off-line scheduling problem a potentially indefinite, periodic processing has to be mapped onto a single time window of a fixed length. We make this new class of applications amenable to constraint programming. We describe which traditional scheduling and real-time computing techniques led to success and which failed when confronted with a large-scale application of this type. Global constraints were used to reduce memory consumption and to speed up computation. An elaborate heuristic, borrowed from Operations Research, was employed to solve the problem. Furthermore, we show that mere serialization is sufficient to find a valid schedule. The actual implementation was done in the concurrent constraint programming language Oz.