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Placing Timely Refreshing Services at the Network Edge

Xishuo Li, Shan Zhang, Hongbin Luo, Xiao Ma, Junyi He

TL;DR

This work forms an integer nonlinear programming problem and proves its NP-hardness, and proposes a lightweighted discounted value approximation (DVA) method, which further decouples the problem in the spatial domain by estimating the offloading costs among edge servers.

Abstract

Accommodating services at the network edge is favorable for time-sensitive applications. However, maintaining service usability is resource-consuming in terms of pulling service images to the edge, synchronizing databases of service containers, and hot updates of service modules. Accordingly, it is critical to determine which service to place based on the received user requests and service refreshing (maintaining) cost, which is usually neglected in existing studies. In this work, we study how to cooperatively place timely refreshing services and offload user requests among edge servers to minimize the backhaul transmission costs. We formulate an integer non-linear programming problem and prove its NP-hardness. This problem is highly non-tractable due to the complex spatial-and-temporal coupling effect among service placement, offloading, and refreshing costs. We first decouple the problem in the temporal domain by transforming it into a Markov shortest-path problem. We then propose a light-weighted Discounted Value Approximation (DVA) method, which further decouples the problem in the spatial domain by estimating the offloading costs among edge servers. The worst performance of DVA is proved to be bounded. 5G service placement testbed experiments and real-trace simulations show that DVA reduces the total transmission cost by up to 59.1% compared with the state-of-the-art baselines.

Placing Timely Refreshing Services at the Network Edge

TL;DR

This work forms an integer nonlinear programming problem and proves its NP-hardness, and proposes a lightweighted discounted value approximation (DVA) method, which further decouples the problem in the spatial domain by estimating the offloading costs among edge servers.

Abstract

Accommodating services at the network edge is favorable for time-sensitive applications. However, maintaining service usability is resource-consuming in terms of pulling service images to the edge, synchronizing databases of service containers, and hot updates of service modules. Accordingly, it is critical to determine which service to place based on the received user requests and service refreshing (maintaining) cost, which is usually neglected in existing studies. In this work, we study how to cooperatively place timely refreshing services and offload user requests among edge servers to minimize the backhaul transmission costs. We formulate an integer non-linear programming problem and prove its NP-hardness. This problem is highly non-tractable due to the complex spatial-and-temporal coupling effect among service placement, offloading, and refreshing costs. We first decouple the problem in the temporal domain by transforming it into a Markov shortest-path problem. We then propose a light-weighted Discounted Value Approximation (DVA) method, which further decouples the problem in the spatial domain by estimating the offloading costs among edge servers. The worst performance of DVA is proved to be bounded. 5G service placement testbed experiments and real-trace simulations show that DVA reduces the total transmission cost by up to 59.1% compared with the state-of-the-art baselines.
Paper Structure (22 sections, 4 theorems, 26 equations, 14 figures, 3 tables, 2 algorithms)

This paper contains 22 sections, 4 theorems, 26 equations, 14 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. System Model
  4. Service Placement and Refreshing Mechanism
  5. Network Model
  6. Service Placement Model
  7. Service Refreshing Model
  8. Problem Formulation and Analysis
  9. Problem Formulation
  10. Hardness of the TRSP Problem
  11. Special Case: Submodular Condition
  12. Algorithms and Solutions
  13. Centralized Algorithm
  14. Distributed Algorithm
  15. Temporal and Spatial Value Approximation
  16. ...and 7 more sections

Key Result

Lemma 1

The TRSP problem is submodular if and only if:

Figures (14)

  • Figure 1: An illustration of the MEC system, the left part presents the service placement and refreshing mechanism.
  • Figure 2: Transforming the TRSP problem into a shortest path problem. Each node consists of service placement, request offloading decisions, and remaining lifetime information. The weight of paths represents the corresponding state transition cost.
  • Figure 3: Comparison with optimal results.
  • Figure 4: Impact of the temporal approximation factor $\theta$.
  • Figure 5: Impact of the spatial approximation factor $\delta$.
  • ...and 9 more figures

Theorems & Definitions (9)

  • Definition 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof