butools.reptrans.FindMarkovianRepresentation¶

butools.reptrans.FindMarkovianRepresentation()¶

Matlab:	mrep = FindMarkovianRepresentation(rep, @transfun, @evalfunc, precision)
Mathematica:	mrep = FindMarkovianRepresentation[rep, transfun, evalfunc, precision]
Python/Numpy:	mrep = FindMarkovianRepresentation(rep, transfun, evalfunc, precision)

Obtains a Markovian representation from a non-Markovian one while keeping the size the same, by applying a series of elementary transformations.

Parameters:

rep : tuple of matrices The initial non-Markovian representation (initial vector and generator of a PH, matrices of a MAP, or a MMAP, etc.) transfun : callable A function that transforms the representation using the given similarity transformation matrix evalfunc : callable A function that returns how far the representation is from the Markovian one precision : double A representation is considered to be a Markovian one if it is closer than the precision. The default value is 1e-7

Returns:

mrep : tuple of matrices The Markovian representation, if found. If not found, the closest one is returned.

Notes

This function should not be called directly. It is used by ‘PHFromME’, ‘MAPFromRAP’, etc. functions.

References

[R13]

G Horváth, M Telek, “A minimal representation of Markov arrival processes and a moments matching method,” Performance Evaluation 64:(9-12) pp. 1153-1168. (2007)