Displaying similar documents to “Simulation of transient performance measures for stiff Markov chains”

Simulation of transient performance measures for stiff markov chains

Abdelaziz Nasroallah (2010)

RAIRO - Operations Research

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We consider the simulation of transient performance measures of high reliable fault-tolerant computer systems. The most widely used mathematical tools to model the behavior of these systems are Markov processes. Here, we deal basically with the simulation of the mean time to failure (MTTF) and the reliability, R(t), of the system at time t. Some variance reduction techniques are used to reduce the simulation time. We will combine two of these techniques: Importance Sampling and...

Central limit theorem for hitting times of functionals of Markov jump processes

Christian Paroissin, Bernard Ycart (2004)

ESAIM: Probability and Statistics

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A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications.

Fast simulation for road traffic network

Roberta Jungblut-Hessel, Brigitte Plateau, William J. Stewart, Bernard Ycart (2001)

RAIRO - Operations Research - Recherche Opérationnelle

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In this paper we present a method to perform fast simulation of large markovian systems. This method is based on the use of three concepts: Markov chain uniformization, event-driven dynamics, and modularity. An application of urban traffic simulation is presented to illustrate the performance of our approach.

Single-use reliability computation of a semi-Markovian system

Guglielmo D'Amico (2014)

Applications of Mathematics

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Markov chain usage models were successfully used to model systems and software. The most prominent approaches are the so-called failure state models Whittaker and Thomason (1994) and the arc-based Bayesian models Sayre and Poore (2000). In this paper we propose arc-based semi-Markov usage models to test systems. We extend previous studies that rely on the Markov chain assumption to the more general semi-Markovian setting. Among the obtained results we give a closed form representation...

Aggregation/disaggregation method for safety models

Štěpán Klapka, Petr Mayer (2002)

Applications of Mathematics

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The paper concerns the possibilities for mathematical modelling of safety related systems (equipment oriented on safety). Some mathematical models have been required by the present European Standards for the railway transport. We are interested in the possibility of using Markov’s models to meet these Standards. In the text an example of using that method in the interlocking equipment life cycle is given. An efficient aggregation/disaggregation method for computing some characteristics...

Hit and run as a unifying device

Hans C. Andersen, Persi Diaconis (2007)

Journal de la société française de statistique

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We present a generalization of hit and run algorithms for Markov chain Monte Carlo problems that is ‘equivalent’ to data augmentation and auxiliary variables. These algorithms contain the Gibbs sampler and Swendsen-Wang block spin dynamics as special cases. The unification allows theorems, examples, and heuristics developed in one domain to illuminate parallel domains.