  We present a site-percolation model based on a modified FCC lattice, as well
as an efficient algorithm of inspecting percolation which takes advantage of
the Markov stochastic theory, in order to study the percolation threshold of
carbon nanotube (CNT) fibers. Our Markov-chain based algorithm carries out the
inspection of percolation by performing repeated sparse matrix-vector
multiplications, which allows parallelized computation to accelerate the
inspection for a given configuration. With this approach, we determine that the
site-percolation transition of CNT fibers occurs at p_c =0.1533+-0.0013, and
analyze the dependence of the effective percolation threshold (corresponding to
0.5 percolation probability) on the length and the aspect ratio of a CNT fiber
on a finite-size-scaling basis. We also discuss the aspect ratio dependence of
percolation probability with various values of p (not restricted to p_c).
