Accession Number : AD0778001

Title :   On the Class of Markov Chains with Finite Convergence Time.

Descriptive Note : Research rept.,

Corporate Author : CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER

Personal Author(s) : Subelman,Eduardo J.

Report Date : FEB 1974

Pagination or Media Count : 23

Abstract : The author studies the necessary and sufficient conditions for a finite ergodic Markov chain to converge in a finite number of transitions to its stationary distribution. Using this result, the class of Markov chains which attain the stationary distribution in a finite number of steps, independent of the initial distribution is described. Then a class of Markov chains exhibiting this property is described. It is shown that a class of queueing models has a Markov chain embedded at the points of regeneration that falls within this class. Finally, the class of continuous time Markov processes whose embedded Markov chain possesses the property of rapid convergence is examined. It is found that, in the case where the distribution of sojourn times is independent of the state, the distribution of the system at time t can be computed in the form of a simple closed expression.

Descriptors :   *Queueing theory, Stochastic processes, Distribution functions, Matrices(Mathematics), Theorems

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE