Edge computing (EC) promises to deliver low-latency and ubiquitous computation to numerous devices at the network edge. This paper aims to jointly optimize edge node (EN) placement and resource allocation for an EC platform, considering demand uncertainty. Diverging from existing approaches treating uncertainties as exogenous, we propose a novel two-stage decision-dependent distributionally robust optimization (DRO) framework to effectively capture the interdependence between EN placement decisions and uncertain demands. The first stage involves making EN placement decisions, while the second stage optimizes resource allocation after uncertainty revelation. We present an exact mixed-integer linear program reformulation for solving the underlying ``min-max-min" two-stage model. We further introduce a valid inequality method to enhance computational efficiency, especially for large-scale networks. Extensive numerical experiments demonstrate the benefits of considering endogenous uncertainties and the advantages of the proposed model and approach.

翻译：边缘计算（EC）有望在网络边缘为大量设备提供低延迟和普适计算服务。本文针对边缘计算平台，考虑需求不确定性，旨在联合优化边缘节点（EN）部署与资源分配。与现有将不确定性视为外生变量的方法不同，我们提出了一种新颖的两阶段决策依赖分布式鲁棒优化（DRO）框架，以有效捕捉边缘节点部署决策与不确定需求之间的相互依赖关系。第一阶段涉及边缘节点部署决策，而第二阶段则在不确定性揭示后优化资源分配。我们提出精确的混合整数线性规划重构以求解所提出的"最小-最大-最小"两阶段模型。为进一步提升计算效率（尤其适用于大规模网络），我们引入了一种有效不等式方法。大量数值实验证明了考虑内生不确定性的益处以及所提模型与方法的优势。