Efficient engineered systems require scalability. A scalable system has increasing performance with increasing system size. In an ideal case, the increase in performance (e.g., speedup) corresponds to the number of units that are added to the system. However, if multiple units work on the same task, then coordination among these units is required. This coordination can introduce overheads with an impact on system performance. The coordination costs can lead to sublinear improvement or even diminishing performance with increasing system size. However, there are also systems that implement efficient coordination and exploit collaboration of units to attain superlinear improvement. Modeling the scalability dynamics is key to understanding efficient systems. Known laws of scalability, such as Amdahl's law, Gustafson's law, and Gunther's Universal Scalability Law, are minimalistic phenomenological models that explain a rich variety of system behaviors through concise equations. While useful to gain general insights, the phenomenological nature of these models may limit the understanding of the underlying dynamics, as they are detached from first principles that could explain coordination overheads among units. Through a decentralized system approach, we propose a general model based on generic interactions between units that is able to describe, as specific cases, any general pattern of scalability included by previously reported laws. The proposed general model of scalability is built on first principles, or at least on a microscopic description of interaction between units, and therefore has the potential to contribute to a better understanding of system behavior and scalability. We show that this model can be applied to a diverse set of systems, such as parallel supercomputers, robot swarms, or wireless sensor networks, creating a unified view on interdisciplinary design for scalability.

中文翻译：

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计算和机器人的可扩展性

高效的工程系统需要可扩展性。可扩展系统的性能随着系统规模的增加而提高。在理想情况下，性能的提高（例如加速）对应于添加到系统中的单元数。但是，如果多个单元执行相同的任务，则需要这些单元之间的协调。这种协调会引入对系统性能有影响的开销。随着系统规模的增加，协调成本会导致次线性改进甚至降低性能。然而，也有一些系统可以实现有效的协调并利用单元之间的协作来实现超线性改进。对可扩展性动态建模是理解高效系统的关键。已知的可扩展性定律，例如 Amdahl 定律、Gustafson 定律和 Gunther' s Universal Scalability Law，是极简的现象学模型，通过简洁的方程解释了丰富多样的系统行为。虽然有助于获得一般见解，但这些模型的现象学性质可能会限制对潜在动态的理解，因为它们与可以解释单位之间协调开销的第一原则分离。通过分散的系统方法，我们提出了一个基于单元之间通用交互的通用模型，该模型能够在特定情况下描述先前报告的法律所包含的任何一般可扩展性模式。提出的可扩展性一般模型建立在第一原则上，或者至少建立在单元之间相互作用的微观描述上，因此有可能有助于更好地理解系统行为和可扩展性。我们表明该模型可以应用于多种系统，例如并行超级计算机、机器人群或无线传感器网络，为可扩展性的跨学科设计创建统一视图。