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Robust Dynamic Edge Service Placement Under Spatio-Temporal Correlated Demand Uncertainty

Jiaming Cheng, Duong Thuy Anh Nguyen, Duong Tung Nguyen

TL;DR

This work tackles robust edge service placement under spatio-temporal demand uncertainty in a geo-distributed edge environment. It introduces a two-stage, multi-period adaptive robust optimization model that reserves resources upfront and allows dynamic service placement and workload Allocation after uncertainty is revealed, leveraging dynamic uncertainty sets to reduce conservatism. To solve the resulting tri-level problem with integer recourse, the authors propose the Robust Optimal Dynamic (ROD) decomposition algorithm, combining outer and inner master/subproblems and McCormick relaxations to achieve finite convergence. Numerical experiments with realistic topology and demand data show substantial cost reductions and improved adaptability compared with static-ARO and stochastic benchmarks, highlighting the value of incorporating spatial-temporal demand correlations and dynamic placement in edge-provisioning strategies.

Abstract

Edge computing allows Service Providers (SPs) to enhance user experience by placing their services closer to the network edge. Determining the optimal provisioning of edge resources to meet the varying and uncertain demand cost-effectively is a critical task for SPs. This paper introduces a novel two-stage multi-period robust model for edge service placement and workload allocation, aiming to minimize the SP's operating costs while ensuring service quality. The salient feature of this model lies in its ability to enable SPs to utilize dynamic service placement and leverage spatio-temporal correlation in demand uncertainties to mitigate the inherent conservatism of robust solutions. In our model, resource reservation is optimized in the initial stage, preemptively, before the actual demand is disclosed, whereas dynamic service placement and workload allocation are determined in the subsequent stage, following the revelation of uncertainties. To address the challenges posed by integer recourse variables in the second stage of the resulting tri-level adjustable robust optimization problem, we propose a novel iterative, decomposition-based approach, ensuring finite convergence to an exact optimal solution. Extensive numerical results are provided to demonstrate the efficacy of the proposed model and approach.

Robust Dynamic Edge Service Placement Under Spatio-Temporal Correlated Demand Uncertainty

TL;DR

This work tackles robust edge service placement under spatio-temporal demand uncertainty in a geo-distributed edge environment. It introduces a two-stage, multi-period adaptive robust optimization model that reserves resources upfront and allows dynamic service placement and workload Allocation after uncertainty is revealed, leveraging dynamic uncertainty sets to reduce conservatism. To solve the resulting tri-level problem with integer recourse, the authors propose the Robust Optimal Dynamic (ROD) decomposition algorithm, combining outer and inner master/subproblems and McCormick relaxations to achieve finite convergence. Numerical experiments with realistic topology and demand data show substantial cost reductions and improved adaptability compared with static-ARO and stochastic benchmarks, highlighting the value of incorporating spatial-temporal demand correlations and dynamic placement in edge-provisioning strategies.

Abstract

Edge computing allows Service Providers (SPs) to enhance user experience by placing their services closer to the network edge. Determining the optimal provisioning of edge resources to meet the varying and uncertain demand cost-effectively is a critical task for SPs. This paper introduces a novel two-stage multi-period robust model for edge service placement and workload allocation, aiming to minimize the SP's operating costs while ensuring service quality. The salient feature of this model lies in its ability to enable SPs to utilize dynamic service placement and leverage spatio-temporal correlation in demand uncertainties to mitigate the inherent conservatism of robust solutions. In our model, resource reservation is optimized in the initial stage, preemptively, before the actual demand is disclosed, whereas dynamic service placement and workload allocation are determined in the subsequent stage, following the revelation of uncertainties. To address the challenges posed by integer recourse variables in the second stage of the resulting tri-level adjustable robust optimization problem, we propose a novel iterative, decomposition-based approach, ensuring finite convergence to an exact optimal solution. Extensive numerical results are provided to demonstrate the efficacy of the proposed model and approach.

Paper Structure

This paper contains 27 sections, 2 theorems, 37 equations, 11 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. System Model and Problem Formulation
  4. System Model
  5. Deterministic Formulation
  6. Uncertainty Modeling
  7. Static uncertainty set (SUS)
  8. Dynamic uncertainty set (DUS)
  9. Adaptive Robust Optimization Problem Formulation
  10. Solution Approach
  11. Robust Optimal Dynamic Algorithm (ROD)
  12. Outer Master Problem (Outer-MP)
  13. Outer Subproblem
  14. Inner Subproblem
  15. Inner Master problem
  16. ...and 12 more sections

Key Result

Proposition 4.1

For any given set of first-stage decisions $\hat{\mathbf{s}}$, the inner-level procedure in Algorithm ALG:inner_CCG exhibits finite convergence. The number of iterations is bounded by $\mathcal{R}$, where $\mathcal{R}$ represents the total number of discrete points in the set $\Xi$.

Figures (11)

  • Figure 1: Resource trading model
  • Figure 2: System model
  • Figure 3: Uncertainty comparison
  • Figure 4: Flow diagram of the ROD algorithm
  • Figure 5: Time series analysis
  • ...and 6 more figures

Theorems & Definitions (4)

  • Proposition 4.1
  • proof
  • Proposition 4.2
  • proof