IMI/Publicaţii/BASM/Ediţii/BASM n.1 (77), 2015/

Determining the Optimal Evolution Time for Markov Processes with Final Sequence of States

Authors: Alexandru Lazari


This paper describes a class of dynamical stochastic systems that re\-pre\-sents an extension of classical Markov decision processes. The Markov stochastic systems with given final sequence of states and unitary transition time, over a finite or infinite state space, are studied. Such dynamical system stops its evolution as soon as given sequence of states in given order is reached. The evolution time of the stochastic system with fixed final sequence of states depends on initial distribution of the states and probability transition matrix. The considered class of processes represents a ge\-ne\-ra\-li\-za\-tion of zero-order Markov processes, studied in [3]. We are seeking for the optimal initial distribution and optimal probability transition matrix that provide the minimal evolution time for the dynamical system. We show that this problem can be solved using the signomial and geometric programming approaches.

Moldova State University
60 Mateevici str., Chișinău
Republic of Moldova, MD−2009


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