With the massive advancements in processing power, Digital Twins (DTs) have become powerful tools to monitor and analyze physical entities. However, due to the potentially very high number of Physical Systems (PSs) to be tracked and emulated, for instance, in a factory environment or an Internet of Things (IoT) network, continuous twinning might become infeasible. In this paper, a DT system is investigated with a set of random PSs, where the twinning rate is limited due to resource constraints. Three cost functions are considered to quantify and penalize the twinning delay. For these cost functions, the optimal twinning problem under twinning rate constraints is formulated. In a numerical example, the proposed cost functions are evaluated for two, one push-based and one pull-based, benchmark twinning policies. The proposed methodology is the first to investigate the optimal twinning problem with random PSs and twinning rate constraints, and serves as a guideline for real-world implementations on how frequently PSs should be twinned.

翻译：随着处理能力的大幅提升，数字孪生已成为监测和分析物理实体的强大工具。然而，由于需要跟踪和仿真的物理系统数量可能非常庞大（例如在工厂环境或物联网网络中），持续孪生可能变得不可行。本文研究了一个包含一组随机物理系统的数字孪生系统，其中孪生率因资源限制而受限。我们考虑了三种成本函数来量化和惩罚孪生延迟。针对这些成本函数，我们构建了孪生率约束下的最优孪生问题。在一个数值示例中，我们针对两种基准孪生策略（一种基于推送，一种基于拉取）评估了所提出的成本函数。所提出的方法是首个研究具有随机物理系统和孪生率约束的最优孪生问题的工作，并为实际应用中物理系统应多久进行一次孪生提供了指导原则。