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Markov Chain
(redirected from Discrete-time Markov chain)

   Also found in: Dictionary/thesaurus, Medical, Acronyms, Wikipedia 0.01 sec.
Markov chain [′mar‚kȯf ‚chān]
(mathematics)
A Markov process whose state space is finite or countably infinite.

(probability)Markov chain - (Named after Andrei Markov) A model of sequences of events where the probability of an event occurring depends upon the fact that a preceding event occurred.

A Markov process is governed by a Markov chain.

In simulation, the principle of the Markov chain is applied to the selection of samples from a probability density function to be applied to the model. Simscript II.5 uses this approach for some modelling functions.


Markov Chain 

a concept in probability theory that emerged from the works of the Russian mathematician A. A. Markov (the elder) that dealt with the study of sequences of dependent trials and sums of random variables associated with them. The development of the theory of Markov chains facilitated the creation of the general theory of Markov processes.



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2 Notation and definitions Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be a discrete-time Markov chain with a discrete state space S and transition probabilities P(x, y) for x, y [member of] S, where [summation over (y)] [member of]S] P(x, y) = 1 for each x [member of] S.
A sampling of the paper topics: the performace of D-redundant disk systems; X-ray--a tool for automatic measurement of hardware paramenters; workload propagation--overload in bursty servers; and optimal importance sampling for discrete-time Markov chains.
Critically acclaimed text for computer performance analysis-now in its second edition The Second Edition of this now-classic text provides a current and thorough treatment of queuing systems, queuing networks, continuous and discrete-time Markov chains, and simulation.
 
 
 
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