Skip to main content
SpringerLink
Log in

Measuring Adaptability and Reliability of Large Scale Systems

  • Conference paper
  • First Online:
Leveraging Applications of Formal Methods, Verification and Validation: Engineering Principles (ISoLA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12477))

Included in the following conference series:

Abstract

In this paper we propose a metric approach to the analysis and verification of large scale self-organising collective systems. Typically, these systems consist of a large number of agents that have to interact to coordinate their activities and, at the same time, have to adapt their behaviour to the dynamic surrounding environment. It is then natural to apply a probabilistic modelling to these systems and, thus, to use a metric for the comparison of their behaviours. In detail, we introduce the population metric, namely a pseudometric measuring the differences in the probabilistic evolution of two systems with respect to some given requirements. We also use this metric to express the properties of adaptability and reliability of a system, which allow us to identify potential critical issues with respect to perturbations in its initial conditions. Then we show how we can combine our metric with statistical inference techniques to obtain a mathematically tractable analysis of large scale systems. Finally, we exploit mean-field approximations to measure the adaptability and reliability of large scale systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. de Alfaro, L., Henzinger, T.A., Majumdar, R.: Discounting the future in systems theory. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1022–1037. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-45061-0_79

    Chapter  Google Scholar 

  2. Anderson, S., Bredeche, N., Eiben, A., Kampis, G., van Steen, M.: Adaptive collective systems: herding black sheep. Bookprints (2013)

    Google Scholar 

  3. Arjovsky, M., Chintala, S., Bottou, L.: Wasserstein generative adversarial networks. In: Proceedings of ICML 2017, pp. 214–223 (2017). http://proceedings.mlr.press/v70/arjovsky17a.html

  4. Bacci, G., Bacci, G., Larsen, K.G., Mardare, R.: On the total variation distance of semi-Markov chains. In: Pitts, A. (ed.) FoSSaCS 2015. LNCS, vol. 9034, pp. 185–199. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46678-0_12

    Chapter  MATH  Google Scholar 

  5. Bortolussi, L., Hillston, J., Loreti, M.: Fluid approximation of broadcasting systems. Theoret. Comput. Sci. 816, 221–248 (2020). https://doi.org/10.1016/j.tcs.2020.02.020

    Article  MathSciNet  MATH  Google Scholar 

  6. van Breugel, F.: A behavioural pseudometric for metric labelled transition systems. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 141–155. Springer, Heidelberg (2005). https://doi.org/10.1007/11539452_14

    Chapter  Google Scholar 

  7. Bures, T., Plasil, F., Kit, M., Tuma, P., Hoch, N.: Software abstractions for component interaction in the internet of things. Computer 49(12), 50–59 (2016)

    Article  Google Scholar 

  8. Castiglioni, V.: Trace and testing metrics on nondeterministic probabilistic processes. In: Proceedings of EXPRESS/SOS 2018. EPTCS, vol. 276, pp. 19–36 (2018). https://doi.org/10.4204/EPTCS.276.4

  9. Castiglioni, V., Chatzikokolakis, K., Palamidessi, C.: A logical characterization of differential privacy via behavioral metrics. In: Bae, K., Ölveczky, P.C. (eds.) FACS 2018. LNCS, vol. 11222, pp. 75–96. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-02146-7_4

    Chapter  Google Scholar 

  10. Castiglioni, V., Loreti, M., Tini, S.: The metric linear-time branching-time spectrum on nondeterministic probabilistic processes. Theoret. Comput. Sci. 813, 20–69 (2020). https://doi.org/10.1016/j.tcs.2019.09.019

    Article  MathSciNet  MATH  Google Scholar 

  11. Chatzikokolakis, K., Gebler, D., Palamidessi, C., Xu, L.: Generalized bisimulation metrics. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 32–46. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44584-6_4

    Chapter  Google Scholar 

  12. Darling, R., Norris, J.: Differential equation approximations for Markov chains. Probab. Surv. 5, 37–79 (2008). https://doi.org/10.1214/07-PS121

    Article  MathSciNet  MATH  Google Scholar 

  13. De Nicola, R., Loreti, M., Pugliese, R., Tiezzi, F.: A formal approach to autonomic systems programming: the SCEL language. ACM Trans. Auton. Adapt. Syst. 9(2), 7:1–7:29 (2014). https://doi.org/10.1145/2619998

    Article  Google Scholar 

  14. Deng, Y., Chothia, T., Palamidessi, C., Pang, J.: Metrics for action-labelled quantitative transition systems. Electron. Not. Theoret. Comput. Sci. 153(2), 79–96 (2006). https://doi.org/10.1016/j.entcs.2005.10.033

    Article  Google Scholar 

  15. Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Metrics for labeled Markov systems. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 258–273. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48320-9_19

    Chapter  Google Scholar 

  16. Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Metrics for labelled Markov processes. Theoret. Comput. Sci. 318(3), 323–354 (2004). https://doi.org/10.1016/j.tcs.2003.09.013

    Article  MathSciNet  MATH  Google Scholar 

  17. Gulrajani, I., Ahmed, F., Arjovsky, M., Dumoulin, V., Courville, A.C.: Improved training of Wasserstein GANs. In: Proceedings of Advances in Neural Information Processing Systems, pp. 5767–5777 (2017). http://papers.nips.cc/paper/7159-improved-training-of-wasserstein-gans

  18. Kantorovich, L.V.: On the transfer of masses. Dokl. Akad. Nauk 37(2), 227–229 (1942)

    Google Scholar 

  19. Kopetz, H.: Internet of things. In: Kopetz, H. (ed.) Real-Time Systems. Real-Time Systems Series, pp. 307–323. Springer, Boston (2011). https://doi.org/10.1007/978-1-4419-8237-7_13

    Chapter  MATH  Google Scholar 

  20. Latella, D., Loreti, M., Massink, M.: On-the-fly PCTL fast mean-field approximated model-checking for self-organising coordination. Sci. Comput. Program. 110, 23–50 (2015). https://doi.org/10.1016/j.scico.2015.06.009

    Article  Google Scholar 

  21. Le Boudec, J.Y., McDonald, D., Mundinger, J.: A generic mean field convergence result for systems of interacting objects. In: Proceedings of QEST 2007, pp. 3–18. IEEE Computer Society (2007). https://doi.org/10.1109/QEST.2007.8

  22. Rachev, S.T., Klebanov, L.B., Stoyanov, S.V., Fabozzi, F.J.: The Methods of Distances in the Theory of Probability and Statistics. Springer, New York (2013). https://doi.org/10.1007/978-1-4614-4869-3

    Book  MATH  Google Scholar 

  23. Song, L., Deng, Y., Cai, X.: Towards automatic measurement of probabilistic processes. In: Proceedings of QSIC 2007, pp. 50–59 (2007). https://doi.org/10.1109/QSIC.2007.65

  24. Sriperumbudur, B.K., Fukumizu, K., Gretton, A., Schölkopf, B., Lanckriet, G.R.G.: On the empirical estimation of integral probability metrics. Electron. J. Stat. 6, 1550–1599 (2021). https://doi.org/10.1214/12-EJS722

    Article  MathSciNet  MATH  Google Scholar 

  25. Talcott, C., Nigam, V., Arbab, F., Kappé, T.: Formal specification and analysis of robust adaptive distributed cyber-physical systems. In: Bernardo, M., De Nicola, R., Hillston, J. (eds.) SFM 2016. LNCS, vol. 9700, pp. 1–35. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-34096-8_1

    Chapter  Google Scholar 

  26. Thorsley, D., Klavins, E.: Approximating stochastic biochemical processes with Wasserstein pseudometrics. IET Syst. Biol. 4(3), 193–211 (2010). https://doi.org/10.1049/iet-syb.2009.0039

    Article  Google Scholar 

  27. Tolstikhin, I.O., Bousquet, O., Gelly, S., Schölkopf, B.: Wasserstein auto-encoders. In: Proceedings of ICLR 2018 (2018). https://openreview.net/forum?id=HkL7n1-0b

  28. Vallender, S.S.: Calculation of the Wasserstein distance between probability distributions on the line. Theory Probab. Appl. 18(4), 784–786 (1974)

    Article  Google Scholar 

  29. Vaserstein, L.N.: Markovian processes on countable space product describing large systems of automata. Probl. Peredachi Inf. 5(3), 64–72 (1969)

    MATH  Google Scholar 

  30. Villani, C.: Optimal Transport: Old and New, vol. 338. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-71050-9

    Book  MATH  Google Scholar 

  31. Wirsing, M., Hölzl, M., Koch, N., Mayer, P. (eds.): Software Engineering for Collective Autonomic Systems. LNCS, vol. 8998. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16310-9

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Valentina Castiglioni

  2. University of Camerino, Camerino, Italy

    Michele Loreti

  3. University of Insubria, Como, Italy

    Simone Tini

Authors
  1. Valentina Castiglioni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michele Loreti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Simone Tini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Valentina Castiglioni , Michele Loreti or Simone Tini .

Editor information

Editors and Affiliations

  1. University of Limerick and Lero, Limerick, Ireland

    Tiziana Margaria

  2. TU Dortmund, Dortmund, Germany

    Bernhard Steffen

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Castiglioni, V., Loreti, M., Tini, S. (2020). Measuring Adaptability and Reliability of Large Scale Systems. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation: Engineering Principles. ISoLA 2020. Lecture Notes in Computer Science(), vol 12477. Springer, Cham. https://doi.org/10.1007/978-3-030-61470-6_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-61470-6_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-61469-0

  • Online ISBN: 978-3-030-61470-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation