In this paper we propose a unified model of execution that aims to fill the abstraction level gap between the primitives of models of computation and the ones of an MPSoC. This model targets a composable MPSoC platform and supports the sequential, Kahn process networks, and dataflow models. Our model comprises of (1) execution operations implementing the primitives in the models of computation, and (2) a time model of execution of streaming applications on a composable platform. We implement these models of computation with the model of execution, and discuss the trade-offs involved. Case studies on an FPGA prototype of the composable MPSoC demonstrate how the model of execution actually works on a real platform. Furthermore they indicate that multiple applications modeled in KPN and dataflow run composably on the platform. (c) 2013 Elsevier B.V. All rights reserved.