Monotone structure in discrete-event systems
Monotone structure in discrete-event systems
Exact sampling with coupled Markov chains and applications to statistical mechanics
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Tradeoff between accuracy and efficiency in the time-parallel simulation of monotone systems
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Tradeoff between accuracy and efficiency in the time-parallel simulation of monotone systems
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
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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.