Complexity of scheduling real-time tasks subjected to cache-related preemption delays

We consider the computational complexity problems of scheduling hard real-time tasks subjected to cache-related preemption delays upon uniprocessor platforms. Several schedulability analyses have been proposed in the literature to explicitly take into account preemption delays due to loss of cache affinity. But, these previous results do not study the complexity of taking scheduling decisions under preemption delay constraints and only focus on classical real-time schedulers (e.g., Rate Monotonic, Earliest Deadline First). In this paper, we focus on the computational complexity of taking scheduling decisions to meet task deadlines while minimizing cache-related preemption delay effects. We design two basic cache-related scheduling problems that are the most simple NP-hard problems to cover the largest set of intractable real-world cache-related scheduling problems. We establish several NP-hardness results for preemptive systems. These results prove that tighter timing analysis leads in practice to harder real-time scheduling problems. These two basic NP-hard scheduling problems are the following: (i) scheduling with cache-related preemption delays and (ii) scheduling with information about the cache state and the sequence of requested memory blocks for every task. We also prove for the first problem that neither fixed-task nor fixed-job priority-based scheduling algorithms can be optimal.