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Generative Profiling for Soft Real-Time Systems and its Applications to Resource Allocation

Georgiy A. Bondar, Abigail Eisenklam, Yifan Cai, Robert Gifford, Tushar Sial, Linh Thi Xuan Phan, Abhishek Halder

Abstract

Modern real-time systems require accurate characterization of task timing behavior to ensure predictable performance, particularly on complex hardware architectures. Existing methods, such as worst-case execution time analysis, often fail to capture the fine-grained timing behaviors of a task under varying resource contexts (e.g., an allocation of cache, memory bandwidth, and CPU frequency), which is necessary to achieve efficient resource utilization. In this paper, we introduce a novel generative profiling approach that synthesizes context-dependent, fine-grained timing profiles for real-time tasks, including those for unmeasured resource allocations. Our approach leverages a nonparametric, conditional multi-marginal Schrödinger Bridge (MSB) formulation to generate accurate execution profiles for unseen resource contexts, with maximum likelihood guarantees. We demonstrate the efficiency and effectiveness of our approach through real-world benchmarks, and showcase its practical utility in a representative case study of adaptive multicore resource allocation for real-time systems.

Generative Profiling for Soft Real-Time Systems and its Applications to Resource Allocation

Abstract

Modern real-time systems require accurate characterization of task timing behavior to ensure predictable performance, particularly on complex hardware architectures. Existing methods, such as worst-case execution time analysis, often fail to capture the fine-grained timing behaviors of a task under varying resource contexts (e.g., an allocation of cache, memory bandwidth, and CPU frequency), which is necessary to achieve efficient resource utilization. In this paper, we introduce a novel generative profiling approach that synthesizes context-dependent, fine-grained timing profiles for real-time tasks, including those for unmeasured resource allocations. Our approach leverages a nonparametric, conditional multi-marginal Schrödinger Bridge (MSB) formulation to generate accurate execution profiles for unseen resource contexts, with maximum likelihood guarantees. We demonstrate the efficiency and effectiveness of our approach through real-world benchmarks, and showcase its practical utility in a representative case study of adaptive multicore resource allocation for real-time systems.

Paper Structure

This paper contains 21 sections, 2 theorems, 34 equations, 9 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background and Problem Formulation
  3. Stochastic Modeling of Context-Dependent Profiles
  4. Nonparametric Learning
  5. Generative Profiling Algorithm
  6. Conditional MSBP
  7. Leveraging Duality to Solve Conditional MSBP
  8. From Conditional MSBP to Generative Profiling
  9. Effectiveness of generative profiling
  10. Benchmarks, Hardware, and Workload Measurement
  11. Accuracy of Generative Stochastic Model
  12. Resource Allocation with Generative Profiles
  13. Case Study: Dynamic Multicore Resource Allocation
  14. Prototype Implementation in Linux
  15. Experimental evaluation
  16. ...and 6 more sections

Key Result

Theorem 1

The MSB $\bm{M}_{\rm{opt}}$ is the unique minimizer of the relative entropy $\bm{M}\mapsto{\mathrm{D_{KL}}}(\bm{M}\parallel\bm{M}_{{\mathrm{Gibbs}}})$ subject to the observational constraints DiscereteMSBPconstr. $\blacktriangleleft$$\blacktriangleleft$

Figures (9)

  • Figure 1: Effect of CPU frequency, cache, and memory bandwidth on the instruction retirement rate of $\mathsf{fft}$splash2x. The benchmark shows distinct phases, with varying relationships (no effect, linear, nonlinear) between instruction rate and CPU frequency, depending on resource allocation (middle phase).
  • Figure 2: Distributions of microarchitectural execution states (rates of instructions, cache requests and cache misses) of $\mathsf{fft}$ at three time points under two different resource contexts.
  • Figure 3: Our proposed generative profiling algorithm scheme with maximum-likelihood guarantee. From empirical profiles of a task's microarchitectural execution states, conditioned on a sparse set of resource allocations $\mathcal{B}'$, we generate 'synthetic' profiles for the unknown resource allocations.
  • Figure 4: The relationship between a transport plan $\bm{M}$, its projections, and the transport cost $\bm{C}$ for $n_s=3$ empirical distributions $\{\mu_\sigma\}_{\sigma\in\llbracket n_s\rrbracket}$. Unimarginal projections equal the distributions, and for the three arbitrary colored points, $[{\bm{M}}_{i_1,i_2,i_3}]$ encodes the total probability mass transported, and $[{\bm{C}}_{i_1,i_2,i_3}]$ the per-unit cost thereof, along the grey-colored path therebetween. Similarly, the bimarginal projections of $\bm{M}$ and the pairwise cost $c$ pertain to the pairwise sections of the path.
  • Figure 5: Maximum-likelihood synthetic profile (blue), mean synthetic profile (red), and all empirical profiles (grey) for the benchmarks $\mathsf{fft}$ and $\mathsf{canneal}$ when $\beta=(7,\:12,\:2.1)^\top$ on our default experimental platform.
  • ...and 4 more figures

Theorems & Definitions (9)

  • Remark
  • Remark
  • Remark
  • Theorem 1: Relative entropy optimality
  • proof
  • Remark : Geometric interpretation
  • Remark : From exponential to linear complexity
  • Remark : Understanding the maximum-likelihood guarantee
  • Proposition 1