Two-Stage Distributionally Robust Edge Node Placement Under Endogenous Demand Uncertainty
Jiaming Cheng, Duong Thuy Anh Nguyen, Duong Tung Nguyen
TL;DR
The paper addresses the challenge of edge node placement under demand uncertainty that is influenced by deployment decisions. It develops a two-stage distributionally robust optimization framework with a decision-dependent moment-based ambiguity set, capturing how EN placement affects both the mean and variance of demand. An exact three-step reformulation yields a single MILP ($(\mathcal{P}_1')$) and an improved variant using extreme-ray cuts for scalability, complemented by McCormick linearization. Empirical results on networks with $I=15$ areas and $J=10$ ENs show that the proposed approach (DRO-DDU) yields lower (and more stable) costs under variability than baselines, highlighting the practical value of modeling endogenous uncertainty in EC planning.
Abstract
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.