  In this paper, we study the evolution of a Finitary Random Interlacement
(FRI) with respect to the expected length of each fiber. In contrast to the
previously proved phase transition between sufficiently large and small fiber
length, we show that for $d=3,4$, FRI is NOT stochastically monotone as fiber
length increasing. At the same time, numerical evidences still strongly support
the existence of a unique and sharp phase transition on the existence of a
unique infinite cluster, while the critical value for phase transition is
estimated to be an inversely proportional function with respect to the system
intensity.
