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A Hodge-Based Framework for Service Operational Analysis in Serverless Platforms

Gianluca Reali, Mauro Femminella

TL;DR

This paper presents a systematic methodology for analyzing inter-function flows and deriving actionable remediation strategies, including dumping effects to contain the effects of harmonic inefficiencies as an alternative to completely restructure the topological model of the service.

Abstract

In this paper we propose a method for analyzing services deployed in serverless platforms. These services typically consists of orchestrated functions that can exhibit complex and non-conservative information flows due to the interaction of independently deployed functions under coarse-grained control mechanisms. We introduce a topological model of serverless services and make use of the Hodge decomposition to partition observed operational flows into locally correctable components and globally persistent harmonic modes. Our analysis shows that harmonic flows naturally arise from different kind of interactions among functions and should be interpreted as structural properties of serverless systems rather than configuration errors. We present a systematic methodology for analyzing inter-function flows and deriving actionable remediation strategies, including dumping effects to contain the effects of harmonic inefficiencies as an alternative to completely restructure the topological model of the service. Experimental results confirm that the proposed approach can uncover latent architectural structures leading to inefficiencies.

A Hodge-Based Framework for Service Operational Analysis in Serverless Platforms

TL;DR

This paper presents a systematic methodology for analyzing inter-function flows and deriving actionable remediation strategies, including dumping effects to contain the effects of harmonic inefficiencies as an alternative to completely restructure the topological model of the service.

Abstract

In this paper we propose a method for analyzing services deployed in serverless platforms. These services typically consists of orchestrated functions that can exhibit complex and non-conservative information flows due to the interaction of independently deployed functions under coarse-grained control mechanisms. We introduce a topological model of serverless services and make use of the Hodge decomposition to partition observed operational flows into locally correctable components and globally persistent harmonic modes. Our analysis shows that harmonic flows naturally arise from different kind of interactions among functions and should be interpreted as structural properties of serverless systems rather than configuration errors. We present a systematic methodology for analyzing inter-function flows and deriving actionable remediation strategies, including dumping effects to contain the effects of harmonic inefficiencies as an alternative to completely restructure the topological model of the service. Experimental results confirm that the proposed approach can uncover latent architectural structures leading to inefficiencies.
Paper Structure (20 sections, 31 equations, 6 figures, 2 tables)

This paper contains 20 sections, 31 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Combinatorial Hodge theory on graphs and edge flows
  4. Serverless/FaaS computing
  5. Bridging Hodge decomposition with FaaS observability
  6. Algebraic and Mathematical Background
  7. Problem Definition
  8. Proposed Method
  9. Procedure for Hodge Decomposition of Serverless Flows
  10. Construct $B_1, B_2$
  11. Solve $L_0 \phi = B_1 f$
  12. Compute the gradient flow
  13. Solve $L_2 \psi = B_2^\top f$
  14. Compute $f_{\mathrm{curl}} = B_2 \psi$
  15. Compute $h = f - f_{\mathrm{grad}} - f_{\mathrm{curl}}$
  16. ...and 5 more sections

Figures (6)

  • Figure 1: Graph of the running example, including the defined sagas.
  • Figure 2: Flow over edges of the invocation graph of the running example.
  • Figure 3: Graph related to the function pressure case study. The gradient component in shown in blue, the curl component in red, and the harmonic component in green.The thickness of the edges for each color represents the weight of the component within the same decomposed component, not in absolute terms.
  • Figure 4: Gradient, flow, and harmonic components over edges generated by the load modeled over the service graph. On the ordinate the unit of measurement is request/$T$.
  • Figure 5: Graph related to the cold start case study. The gradient component in shown in blue, the curl component in red, and the harmonic component in green. The thickness of the edges for each color represents the weight of the component within the same decomposed component, not in absolute terms.
  • ...and 1 more figures