The execution of multiple multimedia applications on a modern Multi-Processor System-on-Chip (MPSoC) rises up the need of a Run-Time Management (RTM) layer to match hardware and application needs. This paper proposes a novel model for the run-time resource allocation problem taking into account both architectural and application standpoints. Our model considers clustered and non-clustered resources, migration and reconfiguration overheads, quality of service (QoS) and application priorities. A near optimal solution is computed focusing on spatial and computational constraints. Experiments reveal that our first implementation is able to manage tens of applications with an overhead of only fews milliseconds and a memory footprint of less than one hundred KB, thus suitable for usage on real systems.