A model-based framework for the design of a symbolic scheduler for pre-emptive real-time tasks

We had shown in our previous work [7, 9] that supervisory control theory (SCT) of discrete-event systems could be applied for scheduling hard real-time systems. In particular, we had presented a formal framework for the synthesis of real-time schedulers on single processor systems using priority-based supervisory control of timed discrete-event systems (TDES). We had also provided the extension of SCT in designing schedulers for uniform multiprocessor systems [8]. As we had considered discrete time models in our scheduler design, the state sizes were substantially large, and increased exponentially with the number of real-time tasks. In order to reduce the state space explosion problem in our models, we have utilized a modified form of symbolic modeling methodology [3], along with the pre-stable algorithm proposed in [3], for reducing state space while designing schedulers for real-time tasks on uniprocessor systems. The main contribution through this paper has been the development of an informal procedure for uniprocessor scheduler design with reduced state space for preemptive real-time tasks.