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Run-time management of both communication and computation resources in a heterogeneous network-on-chip (NoC) is a challenging task. First, platform resources need to be assigned in a fast and efficient way. Secondly, the resources might need to be reallocated when platform conditions or user requirements change. We developed a run-time resource management scheme that is able to efficiently manage a NoC containing fine grain reconfigurable hardware tiles. This paper details our task assignment heuristic and two run-time task migration mechanisms that deal with the message consistency problem in a NoC. We show that specific reconfigurable hardware support improves the performance of the heuristic and that task migration mechanisms need to be tailored to on-chip networks.