On Optimal Hierarchical Resource Sharing in Open Environments

• This paper presents a new perspective in the context of supporting logical resource sharing under hierarchical scheduling. Our work is motivated from a tradeoff between reducing resource holding times and reducing system load (i.e., the collective processor requirements to guarantee the schedulability of hierarchical scheduling frameworks). We formulate an optimization problem that determines the resource holding times of each individual tasks (and therefore those of subsystems) with the goal of minimizing the system load subject to the system's schedulability. We present efficient algorithms to find an optimal solution to the problem, and we prove their correctness. 

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