  We study modulational instability (MI) in optical fibers with random group
velocity dispersion (GVD) generated by sharply localized perturbations of a
normal GVD fiber that are either randomly or periodically placed along the
fiber and that have random strength. This perturbation leads to the appearance
of low frequency MI side lobes that grow with the strength of the
perturbations, whereas they are faded by randomness in their position. If the
random perturbations exhibit a finite average value, they can be compared with
periodically perturbed fibers, where Arnold tongues appear. In that case,
increased randomness in the strengths of the variations tends to affect the
Arnold tongues less than increased randomness in their positions.
