Performance, Markovian modeling

IV. MARKOVIAN MODELING OF ELECTROLYZER (ELECTROCHEMICAL REACTOR) PERFORMANCE... 

The same is true for re-re and si-si options. The statistical modeling of experimental pentad distribution can be performed by considering a first-order Markovian model. The insertion probability for a si... 

Goel, A.L. and Okumoto, K. 1979. A Markovian model for reliability and other performance measures of software systems. In Proceedings cf the National Computing Conference (New York), vol. 48. 

Horvath, A., Paolieri, M., Ridi, L., Vicario, E. Transient analysis of non-Markovian models using stochastic state classes. In Performance Evaluation (2012)... 

It should be emphasized that for Markovian copolymers a knowledge of the values of structural parameters of such a kind will suffice to find the probability of any sequence Uk, i.e. for an exhaustive description of the microstructure of the chains of these copolymers with a given average composition. As for the composition distribution of Markovian copolymers, this obeys for any fraction of Z-mers the Gaussian formula whose covariance matrix elements are Dap/l where Dap depend solely on the values of structural parameters [2]. The calculation of their dependence on time, and the stoichiometric and kinetic parameters of the reaction system permits a complete statistical description of the chemical structure of Markovian copolymers to be accomplished. The above reasoning reveals to which extent the mathematical modeling of the processes of the copolymer synthesis is easier to perform provided the alternation of units in macromolecules is known to obey Markovian statistics. 

Under current treatment of statistical method a set of the states of the Markovian stochastic process describing the ensemble of macromolecules with labeled units can be not only discrete but also continuous. So, for instance, when the description of the products of living anionic copolymerization is performed within the framework of a terminal model the role of the label characterizing the state of a monomeric unit is played by the moment when this unit forms in the course of a macroradical growth [25]. 

German, R. 2000. Performance Analysis of Communication Systems - Modeling with Non-Markovian Stochastic Petri Nets. New York John Chichester Wiley Sons. 

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