In this paper we present a SystemC-based framework to study the effects of running multi-threaded application software on a multiprocessor platform under the control of one or more abstract real-time operating systems (RTOS's). We propose a modelling framework consisting of basic RTOS service models; scheduling, synchronization, and resource allocation, and a generic task model that is able to model periodic and aperiodic tasks as well as task properties such as varying execution times, offsets, deadlines, and data dependencies. A given multiprocessor system is formed by the composition of RTOS service models and the allocation of tasks (the application software) onto RTOS's. We demonstrate the potential of our approach by simulating and analyzing a small multiprocessor system.