Problem: Modern systems contain parts that are themselves systems. Such complex systems thus have sets of subsystems that have their own variability. These subsystems contribute to the functionality of a whole system-of-systems (SoS). Such systems have a very high degree of variability. Therefore, a modeling technique for the variability of an entire SoS is required to express two different levels of variability: variability of the SoS as a whole and variability of subsystems. If these levels are described together, the model becomes hard to understand. When the variability model of the SoS is described separately, each variability model is represented by a tree structure and these models are combined in a further tree structure. For each node in a variability model, a quantity is assigned to express the multiplicity of its instances per one instance of its parent node. Quantities of the whole system may refer to the number of subsystem instances in the system. From the viewpoint of the entire system, constraints and requirements written in natural language are often ambiguous regarding the quantities of subsystems. Such ambiguous constraints and requirements may lead to misunderstandings or conflicts in an SoS configuration. Approach: A separate notion is proposed for variability of an SoS; one model considers the SoS as an undivided entity, while the other considers it as a combination of subsystems. Moreover, a domain-specific notation is proposed to express relationships among the variability properties of systems, to solve the ambiguity of quantities and establish the total validity. This notation adapts an approach, named Pincer Movement, which can then be used to automatically deduce the quantities for the constraints and requirements. Validation: The descriptive capability of the proposed notation was validated with four examples of cloud providers. In addition, the proposed method and description tool were validated through a simple experiment on describing variability models with real practitioners.

中文翻译：

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System-of-Systems 可变性模型中的处理数量

问题：现代系统包含本身就是系统的部分。因此，这种复杂的系统具有一组具有自身可变性的子系统。这些子系统有助于整个系统系统 (SoS) 的功能。这样的系统具有非常高的可变性。因此，需要一种针对整个 SoS 可变性的建模技术来表达两个不同级别的可变性：SoS 作为一个整体的可变性和子系统的可变性。如果将这些级别一起描述，则模型变得难以理解。当单独描述 SoS 的可变性模型时，每个可变性模型都由一个树结构表示，并且这些模型组合成一个进一步的树结构。对于可变性模型中的每个节点，分配一个数量来表示每个父节点实例的多重性。整个系统的数量可以指系统中子系统实例的数量。从整个系统的角度来看，用自然语言编写的约束和要求对于子系统的数量往往是模棱两可的。这种模棱两可的约束和要求可能会导致 SoS 配置中的误解或冲突。方法：针对 SoS 的可变性提出了一个单独的概念；一种模型将 SoS 视为一个不可分割的实体，而另一种则将其视为子系统的组合。此外，提出了一种特定领域的符号来表达系统可变性属性之间的关系，以解决数量的模糊性并建立总有效性。该符号采用了一种名为 Pincer Movement 的方法，然后可用于自动推断约束和要求的数量。验证：提议的符号的描述能力已通过四个云提供商示例进行了验证。此外，所提出的方法和描述工具通过与真实从业者描述可变性模型的简单实验得到验证。