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Sustainable Placement with Cost Minimization in Wireless Digital Twin Networks

Yuzhi Zhou, Yaru Fu, Zheng Shi, Kevin Hung, Tony Q. S. Quek, Yan Zhang

TL;DR

An improved local search algorithm is proposed for this DT placement-driven cost optimization problem as a deterministic integer linear programming (ILP) problem using the sample average approximation (SAA) approach and it is proved that the transformed problem remains NP-hard and thus finding a global optimal solution is very difficult.

Abstract

Digital twin (DT) technology has a high potential to satisfy different requirements of the ever-expanding new applications. Nonetheless, the DT placement in wireless digital twin networks (WDTNs) poses a significant challenge due to the conflict between unpredictable workloads and the limited capacity of edge servers. In other words, each edge server has a risk of overload when handling an excessive number of tasks or services. Overload risks can have detrimental effects on a network's sustainability, yet this aspect is often overlooked in the literature. In this paper, we aim to study the sustainability-aware DT placement problem for WDTNs from a cost minimization perspective. To this end, we formulate the DT placement-driven cost optimization problem as a chance-constrained integer programming problem. For tractability, we transform the original non-deterministic problem into a deterministic integer linear programming (ILP) problem using the sample average approximation (SAA) approach. We prove that the transformed problem remains NP-hard and thus finding a global optimal solution is very difficult. To strike a balance between time efficiency and performance guarantee, we propose an improved local search algorithm for this ILP by identifying high-quality starting states from historical search data and enhancing the search process. Numerical results show a lower cost and higher efficiency of our proposed method compared with the previous schemes.

Sustainable Placement with Cost Minimization in Wireless Digital Twin Networks

TL;DR

An improved local search algorithm is proposed for this DT placement-driven cost optimization problem as a deterministic integer linear programming (ILP) problem using the sample average approximation (SAA) approach and it is proved that the transformed problem remains NP-hard and thus finding a global optimal solution is very difficult.

Abstract

Digital twin (DT) technology has a high potential to satisfy different requirements of the ever-expanding new applications. Nonetheless, the DT placement in wireless digital twin networks (WDTNs) poses a significant challenge due to the conflict between unpredictable workloads and the limited capacity of edge servers. In other words, each edge server has a risk of overload when handling an excessive number of tasks or services. Overload risks can have detrimental effects on a network's sustainability, yet this aspect is often overlooked in the literature. In this paper, we aim to study the sustainability-aware DT placement problem for WDTNs from a cost minimization perspective. To this end, we formulate the DT placement-driven cost optimization problem as a chance-constrained integer programming problem. For tractability, we transform the original non-deterministic problem into a deterministic integer linear programming (ILP) problem using the sample average approximation (SAA) approach. We prove that the transformed problem remains NP-hard and thus finding a global optimal solution is very difficult. To strike a balance between time efficiency and performance guarantee, we propose an improved local search algorithm for this ILP by identifying high-quality starting states from historical search data and enhancing the search process. Numerical results show a lower cost and higher efficiency of our proposed method compared with the previous schemes.
Paper Structure (20 sections, 1 theorem, 24 equations, 10 figures, 2 tables, 1 algorithm)

This paper contains 20 sections, 1 theorem, 24 equations, 10 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Offloading Cost
  5. Communication Cost
  6. Computation Cost
  7. Problem Formulation
  8. Problem Transformation and Complexity Analysis
  9. Problem Transformation
  10. Complexity Analysis
  11. Algorithm Design
  12. Overview of the Proposed Algorithm
  13. Details of the Proposed Algorithm
  14. Phase I of the $t$-th iteration
  15. Phase II of the $t$-th iteration
  16. ...and 5 more sections

Key Result

Theorem 1

$\mathcal{P}_{2}$ is NP-hard.

Figures (10)

  • Figure 1: System model of WDTNs.
  • Figure 2: The $t$-th iteration of our improved local search algorithm.
  • Figure 3: Convergence of average cost with a range of 1-3 components.
  • Figure 4: Convergence of average cost with a range of 1-5 components.
  • Figure 5: Average cost per edge server versus the number of physical devices, wherein the number of edge servers is 6 and the number of components per physical device ranges from 1 to 3.
  • ...and 5 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof