This paper studies the favorite machine model, where each machine has different speed for different types of jobs. The model is a natural generalization of the two related machines model and captures the features of some real life problems, such as the CPU–GPU task scheduling, the two products scheduling and the cloud computing task scheduling. We are interested in the game-theoretic version of the scheduling problem in which jobs correspond to self-interested users and machines correspond to resources. The goal is to design coordination mechanisms (local policies) with a small price of anarchy (PoA) for the scheduling game of favorite machines. We first analyze the well known Makespan policy for our problem, and provide exact bounds on both the PoA and the strong PoA (SPoA). We also propose a new local policy, called FF-LPT, which outperforms several classical policies (e.g., LPT, SPT, FF-SPT and Makespan) in terms of the PoA, and guarantees fast convergence to a pure Nash equilibrium. Moreover, computational results show that the FF-LPT policy also dominates other policies for random instances, and reveal some insights for practical applications.

中文翻译：

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使用喜欢的机器调度自私作业的协调机制

本文研究了最喜欢的机器模型，其中每台机器针对不同类型的作业具有不同的速度。该模型是两个相关机器模型的自然概括，并捕获了一些实际问题的特征，例如CPU-GPU任务调度，两个产品调度和云计算任务调度。我们对调度问题的博弈论版本感兴趣，在该版本中，工作对应于自利项目用户和机器对应于资源。我们的目标是设计一种协调机制（本地策略），以低价的无政府状态（PoA）来安排喜欢的机器的调度游戏。我们首先分析众所周知的Makespan策略来解决我们的问题，并提供PoA和强PoA（SPoA）的确切界限。我们还提出了一项新的地方政策，称为FF-LPT，就PoA而言，它胜过了几种经典政策（例如LPT，SPT，FF-SPT和Makespan），并保证了快速收敛到纯Nash平衡。此外，计算结果表明，FF-LPT策略在随机实例中也主导了其他策略，并揭示了一些实际应用的见解。