Finding cyclic behavior in multiprocessor real-time scheduling

This paper concerns sets of periodic independent real-time tasks with hard deadlines, in a multiprocessor context. We address the cyclicity problem for global multiprocessor schedul-ing. Our aim is to prove the existence of a steady state after a transcient state in valid sched-ules. This could be helpfull for performing exact schedulability tests as well as for the sake of simulation. First, we underline the main differences between the uniprocessor and the multiprocessor cases. Then we consider the case of fixed-priority scheduling strategies, and finally, we extend our results to a wider class of scheduling algorithms. And finally, we present some amazing results as to the date of the begining of the steady state