Schedulers are no Prophets

  • Arnd Hartmanns
  • Holger Hermanns
  • Jan KrčálEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9560)


Several formalisms for concurrent computation have been proposed in recent years that incorporate means to express stochastic continuous-time dynamics and non-determinism. In this setting, some obscure phenomena are known to exist, related to the fact that schedulers may yield too pessimistic verification results, since current non-determinism can surprisingly be resolved based on prophesying the timing of future random events. This paper provides a thorough investigation of the problem, and it presents a solution: Based on a novel semantics of stochastic automata, we identify the class of schedulers strictly unable to prophesy, and show a path towards verification algorithms with respect to that class. The latter uses an encoding into the model of stochastic timed automata under arbitrary schedulers, for which model checking tool support has recently become available.



This work is partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center AVACS (SFB/TR 14), by the Czech Science Foundation under grant agreement P202/12/G061, by the EU 7th Framework Programme under grant agreement no. 295261 (MEALS) and 318490 (SENSATION), by the CDZ project 1023 (CAP), and by the CAS/SAFEA International Partnership Program for Creative Research Teams.


  1. 1.
  2. 2.
  3. 3.
    Andel, T.R., Yasinsac, A.: On the credibility of Manet simulations. IEEE Computer 39(7), 48–54 (2006)CrossRefGoogle Scholar
  4. 4.
    Bogdoll, J., Ferrer Fioriti, L.M., Hartmanns, A., Hermanns, H.: Partial Order Methods for Statistical Model Checking and Simulation. In: Bruni, R., Dingel, J. (eds.) FORTE 2011 and FMOODS 2011. LNCS, vol. 6722, pp. 59–74. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  5. 5.
    Bogdoll, J., Hartmanns, A., Hermanns, H.: Simulation and statistical model checking for Modestly nondeterministic models. In: Schmitt, J.B. (ed.) MMB/DFT. LNCS, vol. 7201, pp. 249–252. Springer, Heidelberg (2012)Google Scholar
  6. 6.
    Bohnenkamp, H.C., D’Argenio, P.R., Hermanns, H., Katoen, J.-P.: MoDeST: a compositional modeling formalism for hard and softly timed systems. IEEE Trans. Software Eng. 32(10), 812–830 (2006)CrossRefGoogle Scholar
  7. 7.
    Bravetti, M., D’Argenio, P.R.: Tutte le algebre insieme: concepts, discussions and relations of stochastic process algebras with general distributions. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P., Siegle, M. (eds.) Validation of Stochastic Systems. LNCS, vol. 2925, pp. 44–88. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  8. 8.
    Bravetti, M., Gorrieri, R.: The theory of interactive generalized semi-Markov processes. Theor. Comput. Sci. 282(1), 5–32 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Cavin, D., Sasson, Y., Schiper, A.: On the accuracy of MANET simulators. In: POMC, pp. 38–43. ACM (2002)Google Scholar
  10. 10.
    D’Argenio, P.R., Katoen, J.-P.: A theory of stochastic systems, part I: stochastic automata. Inf. Comput. 203(1), 1–38 (2005)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    D’Argenio, P.R., Katoen, J.-P.: A theory of stochastic systems, part II: process algebra. Inf. Comput. 203(1), 39–74 (2005)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Giro, S., D’Argenio, P.R.: Quantitative model checking revisited: neither decidable nor approximable. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 179–194. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  13. 13.
    Haas, P.J., Shedler, G.S.: Regenerative generalized semi-Markov processes. Commun. Stat. Stoch. Models 3(3), 409–438 (1987)zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Hahn, E.M., Hartmanns, A., Hermanns, H.: Reachability and reward checking for stochastic timed automata. In: ECEASST, 70 (2014)Google Scholar
  15. 15.
    Harrison, P.G., Strulo, B.: SPADES - a process algebra for discrete event simulation. J. Log. Comput. 10(1), 3–42 (2000)zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Hartmanns, A., Hermanns, H.: The Modest Toolset: an integrated environment for quantitative modelling and verification. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014 (ETAPS). LNCS, vol. 8413, pp. 593–598. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  17. 17.
    Hartmanns, A., Timmer, M.: Sound statistical model checking for MDP using partial order and confluence reduction. STTT 17(4), 429–456 (2015)CrossRefGoogle Scholar
  18. 18.
    Hermanns, H., Krčál, J., Křetínský, J.: Probabilistic bisimulation: naturally on distributions. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 249–265. Springer, Heidelberg (2014) Google Scholar
  19. 19.
    Kurkowski, S., Camp, T., Colagrosso, M.: MANET simulation studies: the incredibles. Mob. Comput. Commun. Rev. 9(4), 50–61 (2005)CrossRefGoogle Scholar
  20. 20.
    Kwiatkowska, M.Z., Norman, G., Parker, D., Sproston, J.: Performance analysis of probabilistic timed automata using digital clocks. Formal Methods Syst. Design 29(1), 33–78 (2006)zbMATHCrossRefGoogle Scholar
  21. 21.
    Matthes, K.: Zur Theorie der Bedienungsprozesse. In: Transactions of the 3rd Prague Conference on Information Theory, Statistics Decision Functions and Random Processes, pp. 513–528 (1962)Google Scholar
  22. 22.
    Nielson, F., Nielson, H.R., Zeng, K.: Stochastic model checking of the stochastic quality calculus. In: De Nicola, R., Hennicker, R. (eds.) Wirsing Festschrift. LNCS, vol. 8950, pp. 522–537. Springer, Heidelberg (2015) Google Scholar
  23. 23.
    Pongor, G.: OMNeT: objective modular network testbed. In: MASCOTS, pp. 323–326. The Society for Computer Simulation (1993)Google Scholar
  24. 24.
    Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming, 1st edn. John Wiley & Sons Inc, New York (1994) zbMATHCrossRefGoogle Scholar
  25. 25.
    Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. Ph.D thesis, Laboratory for Computer Science, Massachusetts Institute of Technology (1995)Google Scholar
  26. 26.
    Stojmenovic, I.: Simulations in wireless sensor and ad hoc networks: matching and advancing models, metrics, and solutions. IEEE Commun. Mag. 46(12), 102–107 (2008)CrossRefGoogle Scholar
  27. 27.
    Strulo, B.: Process algebra for discrete event simulation. Ph.D thesis, Imperial College of Science, Technology and Medicine. University of London, October 1993Google Scholar
  28. 28.
    Timmer, M., van de Pol, J., Stoelinga, M.I.A.: Confluence reduction for Markov automata. In: Braberman, V., Fribourg, L. (eds.) FORMATS 2013. LNCS, vol. 8053, pp. 243–257. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  29. 29.
    Wolovick, N.: Continuous probability and nondeterminism in labeled transaction systems. PhD thesis, Universidad Nacional de Córdoba, Córdoba (2012)Google Scholar
  30. 30.
    Zeng, X., Bagrodia, R., Gerla, M.: GloMoSim: a library for parallel simulation of large-scale wireless networks. In: PADS, pp. 154–161. IEEE Computer Society (1998)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Computer ScienceSaarland UniversitySaarbrückenGermany

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