||In the study of transport properties of randomly layered media, we use the recursive Green's function method and the classical rate equation approach to calculate the channel occupation number and equilibration length. The hopping anisotropy is also included. From the averaged channel occupation number, we find that a transition from ergodic to non-ergodic transport happens. With the introduction of layer randomness, the anisotropic hopping systems is unstable. A dimensional crossover from two-dimensional-like to one-dimension-like transport will occur if the number of layers becomes large. We preliminarily study the transport behaviour in a quasi-periodic system with layer energies arranged in Fibonacci sequence. We find a power law behaviour for the averaged channel occupation number with the increase of number of channels and the index of power lies between zero and one. This indicates an intermediate transport property between anisotropic hopping systems and randomly layered media with isotropic randomness. Finally, from classical rate equations, we derive an analytic formula of sub-equilibration length by using perturbation theory. This formula is compared with sub-equilibration length determined by the recursive Green's function calculation.