System-of-Systems Engineering - Liophant Simulation

What is a Markov Chain• Markov Chains are named after AA Markov, who firstbegan studying them in 1907• A Markov Chain is a mathematical model consisting ofa set of states S={s 1 ,s 2 ,…s m } where the probability oftransitioning between s i and s j at any given time step isp ij , and p ij does not depend on what states have beenvisited prior to the current time step– In other words, the future is dependent only on thepresent and not on the past• Markov PropertyP X i | X = i , X = i ,..., X = i ) = P(X = i | X =(n+1=n+1 n n n−1n−10 0n+1 n+1 nin)Developing Methods and Techniques for System of Systems EngineeringDr. Dimitri Mavris, dimitri.mavris@ae.gatech.edu65