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# Energy-aware scheduling with resource state considerations: Modeling and optimization

**Author**: Ondřej Benedikt

Energy-efficient scheduling has been attracting a considerable amount of attention in recent years. This trend is most likely to continue in the future since energy-efficient scheduling helps to achieve and maintain production sustainability, improve energy efficiency, and reduce energy costs. This thesis focuses on offline energy-efficient scheduling in environments where the state of the resource changes in time and influences energy consumption. Examples of such resources include industrial furnaces used for steel hardening, manufacturing equipment (e.g., CNC), or even embedded electronic systems on a chip.We focus especially on the modeling of the resource state and design of energy-aware optimization methods, including the integration of the resource model into the methods.The goal is to show how suitable resource modeling combined with an appropriate optimization method can improve state-of-the-art solutions.To reach that goal, we study three use-case problems representing samples of both theoretical and practical problems involving offline energy-aware scheduling with a complex resource model.

The first problem is motivated by the steel-hardening production line in Škoda Auto. The objective is to analyze and model the hardening furnace and propose an optimization method to minimize energy consumption during the time intervals when the furnace is idle. The second problem involves a general resource that can be characterized by the finite state machine in the environment where the energy prices change in time. Again, the goal is to have an optimization method incorporating the finite state machine model of the resource that would optimize overall energy consumption cost. Finally, the third problem defined by Honeywell company, involves energy-efficient scheduling of safety-critical tasks on a multiprocessor system on a chip under temporal isolation constraints.

Considering our solution approach, we analyze the behavior of the steel-hardening furnace and identify a bilinear system model that can faithfully simulate it. Then, we derive an optimal control of the furnace for any idle interval length. The optimal cost is then abstracted and captured by the so-called idle energy function. Using this abstraction, we propose a scheduling algorithm solving the studied single-machine fixed-sequence scheduling problem in polynomial time complexity. To solve the second problem, we extend the notion of idle energy function to include not only the idle period length but also the energy costs. Then, we propose a mathematical model that efficiently integrates this extended energy function. Finally, to solve the third problem, we analyze the behavior of several real physical platforms mounting modern multiprocessor systems on a chip. Then, we propose several power models and optimization methods and provide a comparative study addressing models fidelity, methods performance, and scalability. The results across all studied problems show that with careful design choices, the optimization performance can be substantially improved, and the state-of-the-art methods used in the respective fields can be outperformed.