research-article

Perfect simulation and monotone stochastic bounds

Authors:

J. M. Fourneau,

J. M. VincentAuthors Info & Claims

ValueTools '07: Proceedings of the 2nd international conference on Performance evaluation methodologies and tools

Article No.: 65, Pages 1 - 10

Published: 22 October 2007 Publication History

Abstract

We combine monotone bounds of Markov chains and the coupling from the past to obtain an exact sampling of a strong stochastic bound of the steady-state distribution for a Markov chain. Stochastic bounds are sufficient to bound any positive increasing rewards on the steady-state such as the loss rates and the average size or delay. We show the equivalence between st-monotonicity and event monotonicity when the state space is endowed with a total ordering and we provide several algorithms to transform a system into a set of monotone events. As we deal with monotone systems, the coupling technique requires less computational efforts for each iteration. Numerical examples show that we can obtain very important speedups.

References

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Digital Library

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T. Dayar, J.-M. Fourneau, N. Pekergin, and J.-M. Vincent. Polynomials of a stochastic matrix and strong stochastic bounds. In Markov Anniversary Meeting, pages 211--228, Charleston, 2006. Celebration of the 100th anniversary of Markov.

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Cited By

Fourneau JQuessette F(2012)Tradeoff between accuracy and efficiency in the time-parallel simulation of monotone systemsProceedings of the 9th European conference on Computer Performance Engineering10.1007/978-3-642-36781-6_6(80-95)Online publication date: 30-Jul-2012
https://dl.acm.org/doi/10.1007/978-3-642-36781-6_6
Kadi IPekergin NVincent J(2009)Different Monotonicity Definitions in Stochastic ModellingProceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications10.1007/978-3-642-02205-0_11(144-158)Online publication date: 9-Jun-2009
https://dl.acm.org/doi/10.1007/978-3-642-02205-0_11
Bušić AGaujal BVincent JBaras J(2008)Perfect simulation and non-monotone Markovian systemsProceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools10.4108/ICST.VALUETOOLS2008.4404(1-10)Online publication date: 20-Oct-2008
https://dl.acm.org/doi/10.4108/ICST.VALUETOOLS2008.4404

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Perfect simulation and monotone stochastic bounds

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Published In

cover image ACM Conferences

ValueTools '07: Proceedings of the 2nd international conference on Performance evaluation methodologies and tools

October 2007

708 pages

ISBN:9789639799004

General Chair:
Peter Glynn
Stanford University

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ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering)

Brussels, Belgium

Publication History

Published: 22 October 2007

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Valuetools07

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Valuetools07: Second International Conference on Performance Evaluation Methodologies and Tools & Workshops

October 22 - 27, 2007

Nantes, France

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ValueTools '07 Paper Acceptance Rate 45 of 83 submissions, 54%;

Overall Acceptance Rate 90 of 196 submissions, 46%

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Cited By

Fourneau JQuessette F(2012)Tradeoff between accuracy and efficiency in the time-parallel simulation of monotone systemsProceedings of the 9th European conference on Computer Performance Engineering10.1007/978-3-642-36781-6_6(80-95)Online publication date: 30-Jul-2012
https://dl.acm.org/doi/10.1007/978-3-642-36781-6_6
Kadi IPekergin NVincent J(2009)Different Monotonicity Definitions in Stochastic ModellingProceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications10.1007/978-3-642-02205-0_11(144-158)Online publication date: 9-Jun-2009
https://dl.acm.org/doi/10.1007/978-3-642-02205-0_11
Bušić AGaujal BVincent JBaras J(2008)Perfect simulation and non-monotone Markovian systemsProceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools10.4108/ICST.VALUETOOLS2008.4404(1-10)Online publication date: 20-Oct-2008
https://dl.acm.org/doi/10.4108/ICST.VALUETOOLS2008.4404

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