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A Practical Near Optimal Deployment of Service Function Chains in Edge-to-Cloud Networks

Rasoul Behravesh, David Breitgand, Dean H. Lorenz, Danny Raz

TL;DR

This paper considers the problem of efficient deployment of Service Function Chains across the physical network, known to be NP-hard, and proposes a novel near-optimal heuristic that is extremely efficient and scalable.

Abstract

Mobile edge computing offers a myriad of opportunities to innovate and introduce novel applications, thereby enhancing user experiences considerably. A critical issue extensively investigated in this domain is efficient deployment of Service Function Chains (SFCs) across the physical network, spanning from the edge to the cloud. This problem is known to be NP-hard. As a result of its practical importance, there is significant interest in the development of high-quality sub-optimal solutions. In this paper, we consider this problem and propose a novel near-optimal heuristic that is extremely efficient and scalable. We compare our solution to the state-of-the-art heuristic and to the theoretical optimum. In our large-scale evaluations, we use realistic topologies which were previously reported in the literature. We demonstrate that the execution time offered by our solution grows slowly as the number of Virtual Network Function (VNF) forwarding graph embedding requests grows, and it handles one million requests in slightly more than 20 seconds for 100 nodes and 150 edges physical topology.

A Practical Near Optimal Deployment of Service Function Chains in Edge-to-Cloud Networks

TL;DR

This paper considers the problem of efficient deployment of Service Function Chains across the physical network, known to be NP-hard, and proposes a novel near-optimal heuristic that is extremely efficient and scalable.

Abstract

Mobile edge computing offers a myriad of opportunities to innovate and introduce novel applications, thereby enhancing user experiences considerably. A critical issue extensively investigated in this domain is efficient deployment of Service Function Chains (SFCs) across the physical network, spanning from the edge to the cloud. This problem is known to be NP-hard. As a result of its practical importance, there is significant interest in the development of high-quality sub-optimal solutions. In this paper, we consider this problem and propose a novel near-optimal heuristic that is extremely efficient and scalable. We compare our solution to the state-of-the-art heuristic and to the theoretical optimum. In our large-scale evaluations, we use realistic topologies which were previously reported in the literature. We demonstrate that the execution time offered by our solution grows slowly as the number of Virtual Network Function (VNF) forwarding graph embedding requests grows, and it handles one million requests in slightly more than 20 seconds for 100 nodes and 150 edges physical topology.
Paper Structure (15 sections, 1 theorem, 6 equations, 7 figures, 3 tables, 2 algorithms)

This paper contains 15 sections, 1 theorem, 6 equations, 7 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Network Model and Problem Definition
  3. Substrate Network
  4. User Requests
  5. Application Model
  6. Problem Definition
  7. Our Solution
  8. Function Placement and Routing
  9. User Allocation and Request Steering
  10. Analysis
  11. Avoiding Path Enumeration
  12. Evaluation
  13. Results
  14. Related Work
  15. Conclusions and Future Work

Key Result

Theorem 1

alg:heur3 runs in $O(\lvert\mathbf{V}\rvert\lvert\mathbf{E}^a\rvert)$ time per user $u$ and, at its conclusion, $\lvert\mathit{RejectedByRounding}\rvert \le 2 \sum_{a \in \mathbf{A}}\lvert\mathbf{V}\rvert\lvert\mathbf{E}\rvert\lvert\mathbf{E}^a\rvert$

Figures (7)

  • Figure 1: Applications topologies: The first node is always the UE, that should be placed at the user location. Similar to MunkRostRackeSchmid-relax-2021MaoSYY-INFOCOM2022, latency constraints are specified between every pair of functions.
  • Figure 2: SFC Deployment Problem (\ref{['prob:sfcd']})
  • Figure 3: Converting demand to resources
  • Figure 4: Geographically "cabdriver" paths. Paths that head-back west towards a destination on the East are invalid.
  • Figure 5: Rejected User Requests for 40N60E topology, for the scenario of Mixed Latency/Relaxed, Zipf (a=1.2), and 2 SFCs
  • ...and 2 more figures

Theorems & Definitions (3)

  • Definition 1
  • Definition 2
  • Theorem 1