On Energy-Optimal Off-Line Scheduling for Fixed-Priority Hard Real-Time Systems On a Variable Speed Processor

Recently, there has been a wide spread of battery-operated embedded computing systems such as mobile and portable devices. For such systems, energy consumption is one of the most important design constraints because the battery operation time is a primary performance measure. Voltage scheduling, which adjusts the processor speed along with the supply voltage dynamically, is an effective technique in reducing the energy consumption of embedded real-time systems. Although many voltage scheduling algorithms have been proposed, there have been few research results known on the problem of energy-optimal off-line voltage scheduling for fixed-priority hard real-time systems. In this paper, we present three new contributions for this under-investigated problem. First, we prove that the problem is NP-hard. Second, we present a fully polynomial time approximation scheme (FPTAS) for the problem. For any ε > 0, the proposed approximation scheme computes a voltage schedule whose energy consumption is at most (1 + ε) times that of the optimal voltage schedule. Furthermore, the running time is bounded by a polynomial function of the number of input jobs and 1/ε. Third, we extend the FPTAS such that the average energy consumption is minimized given an on-line voltage scheduling algorithm and a probabilistic workload of a job set.