  We simulate one-dimensional arrays of tunnel junctions using the kinetic
Monte Carlo method to study charge filling behaviour in the large charging
energy limit. By applying a small fixed voltage bias and varying the offset
voltage, we investigate this behaviour in clean and disordered arrays (both
weak and strong disorder effects). The offset voltage dependent modulation of
the current is highly sensitive to background charge disorder and exhibits
substantial variation depending on the strength of the disorder. We show that
while small fractional charge filling factors are likely to be washed out in
experimental devices due to strong background charge disorder, larger factors
may be observable.
