Recent trends show a steady increase towards concurrently executing more and more applications on a single embedded system. Multi-Processor System-on-Chip (MPSoC) architectures are proposed to allow complex design of embedded systems. This is achieved by integrating as many processing resources as possible on a single chip and therefore enabling the execution of multiple applications on a single embedded System-on-Chip (SoC). Due to cost implications, the applications have to share some resources when executing concurrently on these systems. To fully exploit the computational power of an MPSoC, an application is further split into a number of concurrent tasks. Depending on the intrinsic behavior of an application, its tasks may be either data- or time-interdependent, and accordingly, two different models of computation, namely data-driven and time-driven, are used to implement such an application. Besides this, applications typically have timing requirements expressed in three categories of firm, soft, and non real-time requirements. In a mixed time-criticality system, the applications that execute concurrently on a single embedded platform have widely varying real-time requirements, where resource sharing causes interference between the applications. In order to execute real-time applications on an embedded platform, the system has to be predictable to ensure that the timing requirements of the applications are met. Moreover, to enable independent design, verification, and integration of mixed-criticality applications, the system has to be strongly composable, i.e., concurrently executing applications are temporally isolated in such a way that the actual-case temporal behavior of each application is unaffected at the cycle-level. In this way, temporal interference between the applications is completely prevented. In this dissertation, we address two main challenges in designing and prototyping mixed time-criticality systems: (i) realizing strongly composable Virtual Platforms (VPs) for mixed-criticality embedded systems, and (ii) proposing a uniform abstract execution layer for applications expressed with different models of computation. Here, we target time-driven models of computation and, Kahn Process Network (KPN) and dataflow (specifically, Cyclo-Static DataFlow (CSDF)) as the two variants of data-driven models of computation. On the basis of these challenges we answer the main research question of how to design and execute multiple applications concurrently on an embedded system, given that the applications are realized with different models of computation and having different levels of time-criticality? This dissertation proposes a solution to create a VP for every application by virtualizing all the hardware resources that are involved in the execution of the applications. For this, a temporal partitioning technique is applied to the CompSOC hardware architecture. On top of this architecture, the CoMik microkernel is designed as a minimum privileged software layer to provide resource partitioning. CoMik creates, controls and schedules processor partitions, and executes an application in its partition by virtualizing the processor’s software hooks, offering an Application Programming Interface (API) to each application to use its allocated resources. Applications can therefore execute directly on their virtual platforms in the same manner as on a dedicated hardware platform. However there exists an execution abstraction gap between the models of computation’s semantics and the platform’s primitive operations. To fill this gap, a model of execution is proposed to define a common set of execution operations and their orchestrations in order to implement an specific model of computation. The model of execution is implemented in the form of a lightweight operating system library, namely CompOSe, which is instantiated in every partition of a VP. CompOSe is designed in a number of software units and is implemented in such a way that it does not introduce any unpredictability in executing an application and complies with the composability property of the system provided by the CoMik microkernel. We demonstrate that our proposed technique enables concurrent composable, predictable execution of applications realized with multiple models of computation by using two experimentation setups. One, a Matlab simulation environment is used to investigate the temporal behavior of the CoMik microkernel. Two, an FPGA prototype of the CompSOC platform is used to study the composability property and support of multiple models of computation by the CompOSe Real-Time Operating System.