Abstract: A real-time application is often modelled as a pipeline of tasks, to be executed on a multi-processor system. The pipeline is periodically activated, and each instance must be completed before an end-to-end deadline. Three important problems must be solved by real-time designers: how to allocate tasks to processors, how to assign scheduling parameters to tasks, and how to guarantee than every pipeline will always complete within its deadline. In the literature, often these three interrelated problems have been tackled separately. In this paper, we use a component-based approach to the overall problem, and propose to analyse each pipeline in isolation. Starting from an algorithm for assigning intermediate deadlines to tasks called ORDER, we derive a simple expression that bounds the total amount of bandwidth to be allocated to the pipeline, and use such expression as a basis allocating the pipeline's tasks onto the available processors.