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This paper proposes a duplication based algorithm called integrated duplication based scheduling algorithm (InDuSA) capable of scheduling hard and soft real-time tasks and messages on precedence related NOWs. The system is heterogeneous in that a task can have diverse execution times on different workstations. Given a mix of hard and soft real-time tasks, our algorithm assigns higher priority to hard tasks. Once the tasks are scheduled, the proposed scheme duplicates certain tasks. Doing so reduces the inter-processor communication time between communicating tasks assigned to different workstations. This enables certain tasks to start (and finish) earlier. Hence, the schedulability increases. Moreover, the proposed scheme is scalable in that it can generate a schedule even if a sufficient number of processors are not available. Initial simulation results suggest that the proposed scheme offers better schedulability as compared to other algorithms in the literature when there is significant communication in the system.