Classical task scheduling employs a very simplified model of the target parallel system. Experiments demonstrated that this leads to inaccurate and inefficient schedules. Contention aware scheduling heuristics take the contention for communication resources into account, which improves the schedules significantly. Yet, one aspect remains to be investigated: the involvement of the processors in communication. This paper proposes a new scheduling model, called involvement-contention model, that integrates the consideration for the processor involvement into task scheduling. A list scheduling based heuristic is proposed for the new model, which produces significantly more accurate and efficient schedules in experiments on real parallel systems.