In this paper, we extend the compositional scheduling framework to enable the integration of an existing (legacy) application as a component on a faster processor which needs to be shared with other components. After admission of this application into the framework, the integrated component still has to satisfy its tasks' deadline constraints and it must execute jobs in the same order as it did previously on the dedicated processor, regardless of the actual supply of processor resources. We propose a method - called virtual scheduling - which establishes this by reconstructing an appropriate order of delivering events. Virtual scheduling is therefore independent of the component-level scheduling policy and it is transparent to a component, so that it is even applicable without making modifications to the code or specification of the application.