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A framework to measure the robustness of programs in the unpredictable environment

Valentina Castiglioni, Michele Loreti, Simone Tini

TL;DR

A framework that allows us to measure the robustness of systems and expresses the ability of a program to maintain its intended behaviour despite the presence of perturbations in the environment is presented.

Abstract

Due to the diffusion of IoT, modern software systems are often thought to control and coordinate smart devices in order to manage assets and resources, and to guarantee efficient behaviours. For this class of systems, which interact extensively with humans and with their environment, it is thus crucial to guarantee their correct behaviour in order to avoid unexpected and possibly dangerous situations. In this paper we will present a framework that allows us to measure the robustness of systems. This is the ability of a program to tolerate changes in the environmental conditions and preserving the original behaviour. In the proposed framework, the interaction of a program with its environment is represented as a sequence of random variables describing how both evolve in time. For this reason, the considered measures will be defined among probability distributions of observed data. The proposed framework will be then used to define the notions of adaptability and reliability. The former indicates the ability of a program to absorb perturbation on environmental conditions after a given amount of time. The latter expresses the ability of a program to maintain its intended behaviour (up-to some reasonable tolerance) despite the presence of perturbations in the environment. Moreover, an algorithm, based on statistical inference, is proposed to evaluate the proposed metric and the aforementioned properties. We use two case studies to the describe and evaluate the proposed approach.

A framework to measure the robustness of programs in the unpredictable environment

TL;DR

A framework that allows us to measure the robustness of systems and expresses the ability of a program to maintain its intended behaviour despite the presence of perturbations in the environment is presented.

Abstract

Due to the diffusion of IoT, modern software systems are often thought to control and coordinate smart devices in order to manage assets and resources, and to guarantee efficient behaviours. For this class of systems, which interact extensively with humans and with their environment, it is thus crucial to guarantee their correct behaviour in order to avoid unexpected and possibly dangerous situations. In this paper we will present a framework that allows us to measure the robustness of systems. This is the ability of a program to tolerate changes in the environmental conditions and preserving the original behaviour. In the proposed framework, the interaction of a program with its environment is represented as a sequence of random variables describing how both evolve in time. For this reason, the considered measures will be defined among probability distributions of observed data. The proposed framework will be then used to define the notions of adaptability and reliability. The former indicates the ability of a program to absorb perturbation on environmental conditions after a given amount of time. The latter expresses the ability of a program to maintain its intended behaviour (up-to some reasonable tolerance) despite the presence of perturbations in the environment. Moreover, an algorithm, based on statistical inference, is proposed to evaluate the proposed metric and the aforementioned properties. We use two case studies to the describe and evaluate the proposed approach.
Paper Structure (25 sections, 9 theorems, 47 equations, 19 figures, 1 table)

This paper contains 25 sections, 9 theorems, 47 equations, 19 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. The model
  4. Modelling the data space
  5. Modelling processes
  6. Modelling the environment
  7. Modelling system's behaviour
  8. Towards a metric for systems
  9. A metric on data states
  10. Lifting mD to distributions
  11. The evolution metric
  12. Estimating the evolution metric
  13. Computing empirical evolution sequences
  14. Computing distance between two configurations
  15. Analysis of the three-tanks experiment
  16. ...and 10 more sections

Key Result

Proposition 3.7

Let $P \in \mathcal{P}$ and $\mathbf{d} \in \mathcal{D}$. Then $\mathsf{pstep}(P,\mathbf{d})$ is a distribution with finite support, namely the set $\mathsf{supp}(\mathsf{pstep}(P,\mathbf{d}))=\{ (\theta,P') \mid (\mathsf{pstep}(P,\mathbf{d}))(\theta,P') >0\}$ is finite and $\sum_{(\theta,P')\in\mat

Figures (19)

  • Figure 1: Schema of the three-tanks scenario.
  • Figure 2: Functions used to simulate behaviour of a configuration.
  • Figure 3: Function used to obtain $N$ samples of the evolution sequence of a configuration.
  • Figure 4: Simulation results. The dashed red line corresponds to $l_{goal} = 10$.
  • Figure 5: Simulation of the variation of the level of water in each tank in the two scenarios. The dashed green line corresponds to $l_{goal} = 10$.
  • ...and 14 more figures

Theorems & Definitions (42)

  • Remark 1.1
  • Remark 1.2
  • Definition 2.2: Wasserstein hemimetric
  • Remark 2.3
  • Example 3.2
  • Definition 3.3: Data space
  • Example 3.4
  • Definition 3.5: Data state
  • Definition 3.6: Syntax of processes
  • Proposition 3.7: Properties of process semantics
  • ...and 32 more