Conventional cache models are not suited for real-time parallel processing because tasks may flush each other's data out of the cache in an unpredictable manner. In this way the system is not compositional so the overall performance is difficult to predict and the integration of new tasks expensive. This paper proposes a new method that imposes compositionality to the system?s performance and makes different memory hierarchy optimizations possible for multimedia communicating tasks when running on embedded multiprocessor architectures. The method is based on a cache allocation strategy that assigns sets of the unified cache exclusively to tasks and to the communication buffers. We also analytically formulate the problem and describe a method to compute the cache partitioning ratio for optimizing the throughput and the consumed power. When applied to a multiprocessor with memory hierarchy our technique delivers also performance gain. Compared to the shared cache case, for an application consisting of two jpeg decoders and one edge detection algorithm 5 times less misses are experienced and for an mpeg2 decoder 6.5 times less misses are experienced.