Advertisement

Speed-Up of Stochastic Simulation of PCTMC Models by Statistical Model Reduction

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9272)

Abstract

We present a novel statistical model reduction method which can significantly boost the speed of stochastic simulation of a population continuous-time Markov chain (PCTMC) model. This is achieved by identifying and removing agent types and transitions from the simulation which have only minor impact on the evolution of population dynamics of target agent types specified by the modeller. The error induced on the target agent types can be measured by a normalized coupling coefficient, which is calculated by an error propagation method over a directed relation graph for the PCTMC, using a limited number of simulation runs of the full model. Those agent types and transitions with minor impact are safely removed without incurring a significant error on the simulation result. To demonstrate the approach, we show the usefulness of our statistical reduction method by applying it to 50 randomly generated PCTMC models corresponding to different city bike-sharing scenarios.

Keywords

Stochastic Simulation Reduction Algorithm Agent Type Continuous Time Markov Chain Broadcast Message 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Allen, L.J., Allen, E.J.: A comparison of three different stochastic population models with regard to persistence time. Theoretical Population Biology 64(4), 439–449 (2003)CrossRefMATHGoogle Scholar
  2. 2.
    Calder, M., Vyshemirsky, V., Gilbert, D., Orton, R.: Analysis of Signalling Pathways Using Continuous Time Markov Chains. In: Priami, C., Plotkin, G. (eds.) Transactions on Computational Systems Biology VI. LNCS (LNBI), vol. 4220, pp. 44–67. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  3. 3.
    Cerotti, D., Gribaudo, M., Bobbio, A.: Markovian agents models for wireless sensor networks deployed in environmental protection. Rel. Eng. & Sys. Safety 130, 149–158 (2014)CrossRefGoogle Scholar
  4. 4.
    Tribastone, M., Gilmore, S., Hillston, J.: Scalable differential analysis of process algebra models. IEEE Transactions on Software Engineering 38(1), 205–219 (2012)CrossRefGoogle Scholar
  5. 5.
    Guenther, M.C., Stefanek, A., Bradley, J.T.: Moment Closures for Performance Models with Highly Non-linear Rates. In: Tribastone, M., Gilmore, S. (eds.) UKPEW 2012 and EPEW 2012. LNCS, vol. 7587, pp. 32–47. Springer, Heidelberg (2013)Google Scholar
  6. 6.
    Hillston, J.: Challenges for Quantitative Analysis of Collective Adaptive Systems. In: Abadi, M., Lluch Lafuente, A. (eds.) TGC 2013. LNCS, vol. 8358, pp. 14–21. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  7. 7.
    Lu, T., Law, C.K.: A directed relation graph method for mechanism reduction. Proceedings of the Combustion Institute 30(1), 1333–1341 (2005)CrossRefGoogle Scholar
  8. 8.
    Pepiot-Desjardins, P., Pitsch, H.: An efficient error-propagation-based reduction method for large chemical kinetic mechanisms. Combustion and Flame 154(1), 67–81 (2008)CrossRefMATHGoogle Scholar
  9. 9.
    Niemeyer, K.E., Sung, C.J., Raju, M.P.: Skeletal mechanism generation for surrogate fuels using directed relation graph with error propagation and sensitivity analysis. Combustion and Flame 157(9), 1760–1770 (2010)CrossRefGoogle Scholar
  10. 10.
    Feng, C., Hillston, J.: PALOMA: A Process Algebra for Located Markovian Agents. In: Norman, G., Sanders, W. (eds.) QEST 2014. LNCS, vol. 8657, pp. 265–280. Springer, Heidelberg (2014) Google Scholar
  11. 11.
    Bortolussi, L., Hillston, J., Latella, D., Massink, M.: Continuous approximation of collective system behaviour: A tutorial. Performance Evaluation 70(5), 317–349 (2013)CrossRefGoogle Scholar
  12. 12.
    Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  13. 13.
    Younes, H.L.S., Simmons, R.G.: Probabilistic Verification of Discrete Event Systems Using Acceptance Sampling. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 223–235. Springer, Heidelberg (2002) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LFCS, School of InformaticsUniversity of EdinburghEdinburghScotland, UK

Personalised recommendations