Design-time application mapping is limited to a predefined set of applications and a static platform. Resource management at run-time is required to handle future changes in the application set, and to provide some degree of fault tolerance, due to imperfect production processes and wear of materials. This paper concerns resource allocation at run-time, allowing multiple real-time applications to run simultaneously on a heterogeneous MPSoC. Low-complexity algorithms are required, in order to respond fast enough to unpredictable execution requests. The authors present a decomposition of this problem into four phases. The allocation of tasks to specific locations in the platform is the main contribution of this work.