An exact accelerated stochastic simulation algorithm

Mjolsness, Eric; Orendorff, David; Chatelain, Philippe; Koumoutsakos, Petros

doi:10.1063/1.3078490

Cited by 16 publications

(36 citation statements)

References 18 publications

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“…For example, the bounds that Cao et al [7] have proposed may provide a promising avenue for this particular endeavour. Ongoing work aims to extend the present algorithm to spatially developing systems [21] with multiresolution capabilities [4] with delays and in extending the recently proposed exact R-leaping algorithm [18] to systems with delays. …”

Section: Discussionmentioning

confidence: 98%

D-leaping: Accelerating stochastic simulation algorithms for reactions with delays

Bayati

Chatelain

Koumoutsakos

2009

Journal of Computational Physics

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Section: Discussionmentioning

confidence: 98%

D-leaping: Accelerating stochastic simulation algorithms for reactions with delays

Bayati

Chatelain

Koumoutsakos

2009

Journal of Computational Physics

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“…Equations (19) and (20) imply that smaller values of p result in much better approximation. However, a value for p that is too small can make the geometric sampling described by (14) inefficient, as the cumulative probabilities of the form P r(Y s k ≤ n) will involve too many terms.…”

Section: Quality Of Approximationmentioning

confidence: 96%

“…Several accelerated methods have been proposed that are either exact or approximate. Exact methods typically involve optimisations over the standard algorithm, such as the next reaction method [8], the optimised DM [5], the logarithmic DM [17] and ER-leap [19]. Most of these approaches involve the use of appropriate data structures in order to generate the simulation events efficiently.…”

Section: Introductionmentioning

confidence: 99%

Markov Chain Simulation with Fewer Random Samples

Milios

Gilmore

2013

Electronic Notes in Theoretical Computer Science

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We propose an accelerated CTMC simulation method that is exact in the sense that it produces all of the transitions involved. We call our method Trajectory Sampling Simulation as it samples from the distribution of state sequences and the distribution of time given some particular sequence. Sampling from the trajectory space rather than the transition space means that we need to generate fewer random numbers, which is an operation that is typically computationally expensive. Sampling from the time distribution involves approximating the exponential distributions that govern the sojourn times with a geometric distribution. A proper selection for the approximation parameters can ensure that the stochastic process simulated is almost identical to the simulation of the original Markov chain. Our approach does not depend on the properties of the system and it can be used as an alternative to more efficient approaches when those are not applicable.

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“…However, this method has the following drawbacks, such as, it is easily influenced by the random sample size, low efficient and inaccurate calculation results (Peer and Sharma 2007;Mjolsness et al 2009;Sakalauskas 2002). In this article, to solve stochastic models accurately and precisely, a novel two-phase approach is proposed, that is, initially, according to the feature of different removal probability density functions, disassembly probability density functions of feasible disassembly paths are determined by a time-domain method or frequency method, and additionally, after disassembly probability density functions have been obtained, typical stochastic models in the different disassembly decision-making are solved by a numerical solution method.…”

Section: The Minimum Expected Value Model Of Disassembly Timementioning

confidence: 99%

Evaluation model and algorithm of product disassembly process with stochastic feature

Tian

Liu

Tian

et al. 2011

Clean Techn Environ Policy

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Disassembly planning is considered as the optimization of disassembly sequences with the target of the shortest disassembly time, the lowest disassembly cost, and the minimum disassembly energy consumption. However, obsolete products suffer from the influence of a variety of uncertainties, the disassembly process of products has the strong uncertain feature. Traditionally, to account for this uncertainty, each removal operation or removal task is assumed to be an activity or event with certain probability, and the determination of the optimal path of a disassembly process is merely a probabilistic planning problem based on this assumption. In this article, based on the established stochastic disassembly network graph, combined with different disassembly decisionmaking criterion, typical stochastic models for disassembly time analysis are developed. In addition, a two-phase approach is proposed to solve the typical stochastic models. Initially, according to different removal probability density functions, disassembly probability density functions of feasible disassembly paths are determined by a timedomain method or frequency-domain method, and additionally, after the disassembly probability density functions have been obtained, the quantitative evaluation of a product disassembly process and stochastic optimization of feasible disassembly paths are realized by a numerical solution method. Finally, a numerical example is illustrated to test the proposed concepts and the effectiveness of the proposed approach.

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An exact accelerated stochastic simulation algorithm

Cited by 16 publications

References 18 publications

D-leaping: Accelerating stochastic simulation algorithms for reactions with delays

D-leaping: Accelerating stochastic simulation algorithms for reactions with delays

Markov Chain Simulation with Fewer Random Samples

Evaluation model and algorithm of product disassembly process with stochastic feature

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