In this paper, we introduce a new kind of constraints, called core precedence constraints, in a cyclic resource constrained scheduling problem with temporal constraints. We use them to model energy saving in a network scheduling problem. Then we study the impact of these new constraints on an effcient approach for cyclic RCPSP: the decomposed software pipelining approach. After discussion, we show that this approach can be used to prove that even without resource constraint, the existence of a periodic schedule is an NP-complete problem.