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Evaluation of Dynamic Vector Bin Packing for Virtual Machine Placement

Zong Yu Lee, Xueyan Tang

TL;DR

This paper evaluates state-of-the-art MinUsageTime DVBP algorithms in non-clairvoyant, clairvoyant and learning-augmented online settings, where item durations (virtual machine lifetimes) are unknown, known and predicted, respectively.

Abstract

Virtual machine placement is a crucial challenge in cloud computing for efficiently utilizing physical machine resources in data centers. Virtual machine placement can be formulated as a MinUsageTime Dynamic Vector Bin Packing (DVBP) problem, aiming to minimize the total usage time of the physical machines. This paper evaluates state-of-the-art MinUsageTime DVBP algorithms in non-clairvoyant, clairvoyant and learning-augmented online settings, where item durations (virtual machine lifetimes) are unknown, known and predicted, respectively. Besides the algorithms taken from the literature, we also develop several new algorithms or enhancements. Empirical experimentation is carried out with real-world datasets of Microsoft Azure. The insights from the experimental results are discussed to explore the structures of algorithms and promising design elements that work well in practice.

Evaluation of Dynamic Vector Bin Packing for Virtual Machine Placement

TL;DR

This paper evaluates state-of-the-art MinUsageTime DVBP algorithms in non-clairvoyant, clairvoyant and learning-augmented online settings, where item durations (virtual machine lifetimes) are unknown, known and predicted, respectively.

Abstract

Virtual machine placement is a crucial challenge in cloud computing for efficiently utilizing physical machine resources in data centers. Virtual machine placement can be formulated as a MinUsageTime Dynamic Vector Bin Packing (DVBP) problem, aiming to minimize the total usage time of the physical machines. This paper evaluates state-of-the-art MinUsageTime DVBP algorithms in non-clairvoyant, clairvoyant and learning-augmented online settings, where item durations (virtual machine lifetimes) are unknown, known and predicted, respectively. Besides the algorithms taken from the literature, we also develop several new algorithms or enhancements. Empirical experimentation is carried out with real-world datasets of Microsoft Azure. The insights from the experimental results are discussed to explore the structures of algorithms and promising design elements that work well in practice.
Paper Structure (26 sections, 7 theorems, 30 equations, 14 figures)

This paper contains 26 sections, 7 theorems, 30 equations, 14 figures.

Table of Contents

  1. Introduction
  2. Problem Definition and Preliminaries
  3. Experiment Setup
  4. Non-clairvoyant Algorithms
  5. First Fit and Most Recently Used
  6. Next Fit and Round Robin Next Fit
  7. Best Fit
  8. Experimental Comparison in Non-clairvoyant Setting
  9. Clairvoyant Algorithms
  10. Classify By Departure Time
  11. Nearest Remaining Time (NRT)
  12. Greedy
  13. Classify By Duration
  14. Hybrid Algorithm
  15. Experimental Comparison in Clairvoyant Setting
  16. ...and 11 more sections

Key Result

Proposition 1

If $\mathcal{R}'$ is the $\alpha$-extension of $\mathcal{R}$, it holds that $\int_{-\infty}^{\infty}{SS_\infty(\mathcal{R}', t)} \, \mathrm{d}t = \alpha \cdot \int_{-\infty}^{\infty}{SS_\infty(\mathcal{R}, t) \, \mathrm{d}t}$.

Figures (14)

  • Figure 1: Exploratory analysis of VM lifetimes
  • Figure 2: Performance of Best Fit
  • Figure 3: Performance of non-clairvoyant algorithms
  • Figure 4: Performance of Classify-By-Departure-Time
  • Figure 5: Performance of NRT
  • ...and 9 more figures

Theorems & Definitions (11)

  • Proposition 1
  • Proposition 2: Relationship between $\ell_\infty$-norms
  • Proposition 3: Lower bound of $\mathrm{OPT}$
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • ...and 1 more