We demonstrate that, for periodic systems with offsets (tasks or flows of messages within a time-triggered network), the simulation cycle can be confined to the range of [0, hyperperiod) only under the condition that an idle point exists at the hyper-period. Furthermore, we establish that ensuring both (1) contention-freedom and (2) that no offset exceeds the value of the period minus duration, is a sufficient condition to guarantee the presence of an idle point at the hyper-period. Most contemporary methods aiming to eliminate latency are implicitly based on these properties and fail to propose a schedule if the input system does not allow a contention-free solution. Consequently, we propose a heuristic approach to scheduling periodic flows of frames within time-triggered networks. Our method focuses on minimizing latency, without necessitating a solution where every frame at every output port is contention-free, and it effectively manages the cyclicity problem.