System-of-Systems Engineering - Liophant Simulation
System-of-Systems Engineering - Liophant Simulation System-of-Systems Engineering - Liophant Simulation
Markov Chains• A Markov Chain is a directed graph in which theedge weights represent transition probabilities,and the probabilities on the edges leaving avertex sum to 1• Markov chains are used to model stochasticprocesses– For example, a Markov chain can be used to create astochastic version of the SIR model developed usingsystem dynamics– Queuing models– Bacteria growthDeveloping Methods and Techniques for System of Systems EngineeringDr. Dimitri Mavris, dimitri.mavris@ae.gatech.edu66
Markov Chains• The transition probabilitybetween state i and j isdenoted p ij• They are typicallyrepresented in atransition matrix, wherethe rows represent thepresent state and thecolumns represent thestate at the next timestepS1p 21S2p 32p 12 p 23S3Developing Methods and Techniques for System of Systems EngineeringDr. Dimitri Mavris, dimitri.mavris@ae.gatech.edu67
- Page 15 and 16: What is needed for this New Paradig
- Page 17 and 18: An Architecture-based Approach to S
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- Page 23 and 24: Extension to Systems-of-Systems Ana
- Page 25 and 26: Fundamental Properties of a Complex
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- Page 37 and 38: Discrete Event Simulations• Discr
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- Page 45 and 46: Fitting Modal ResponsesDeveloping M
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- Page 57 and 58: Concluding Remarks• System of Sys
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- Page 65: What is a Markov Chain• Markov Ch
Markov Chains• A Markov Chain is a directed graph in which theedge weights represent transition probabilities,and the probabilities on the edges leaving avertex sum to 1• Markov chains are used to model stochasticprocesses– For example, a Markov chain can be used to create astochastic version <strong>of</strong> the SIR model developed usingsystem dynamics– Queuing models– Bacteria growthDeveloping Methods and Techniques for <strong>System</strong> <strong>of</strong> <strong>System</strong>s <strong>Engineering</strong>Dr. Dimitri Mavris, dimitri.mavris@ae.gatech.edu66
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