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.
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References
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)
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)
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)
Tribastone, M., Gilmore, S., Hillston, J.: Scalable differential analysis of process algebra models. IEEE Transactions on Software Engineering 38(1), 205–219 (2012)
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)
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)
Lu, T., Law, C.K.: A directed relation graph method for mechanism reduction. Proceedings of the Combustion Institute 30(1), 1333–1341 (2005)
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)
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)
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)
Bortolussi, L., Hillston, J., Latella, D., Massink, M.: Continuous approximation of collective system behaviour: A tutorial. Performance Evaluation 70(5), 317–349 (2013)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry 81(25), 2340–2361 (1977)
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)
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Feng, C., Hillston, J. (2015). Speed-Up of Stochastic Simulation of PCTMC Models by Statistical Model Reduction. In: Beltrán, M., Knottenbelt, W., Bradley, J. (eds) Computer Performance Engineering. EPEW 2015. Lecture Notes in Computer Science(), vol 9272. Springer, Cham. https://doi.org/10.1007/978-3-319-23267-6_19
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DOI: https://doi.org/10.1007/978-3-319-23267-6_19
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