Hierarchical scheduling is a promising methodology for designing and deploying real-time applications, since it enables component-based design and analysis, and supports temporal isolation among competing applications. In hierarchical scheduling an application is described by means of a temporal interface. The designer faces the problem of how to derive the interface parameters so to make the application schedulable, at the same time minimizing the waste of computational resources. The problem is particularly relevant in multiprocessor systems, where it is not clear yet how the interface parameters influence the schedulability of the application and allocation on the physical platform. In this paper we present three novel contributions to hierarchical scheduling for multiprocessor systems. First, we propose the Bounded-Delay Multipartition (BDM), a new interface specification model that allows the designer to balance resource usage versus flexibility in selecting the virtual platform parameters. Second, we explore the schedulability region of a real-time application on top of a generic virtual platform, and derive the interface parameter. Finally, we propose Fluid Best-Fit, an algorithm that takes advantage of the extra degree of flexibility provided by the BDM to compute the virtual platform parameters and allocate it on the physical platform. The performance of the algorithm is evaluated by simulations.