Dear Rajiv,
The model we present is for a device in the weak coupling limit. In this limit the conductance is proportional to the number of accessible charge states on the device. The number of accessible charge states for given a gate and source-drain voltage are visualized in the charge stability diagram. If n is the number of charge states in the bias window, then the current is given as:
I = a (n-1)
where a is a proportionality factor which depends on the coupling between the island and the source-drain electrodes.
The number of charge states n>0, and only when there are two accesible charge states, is it possible for the electron to jump on and off the island.
Hope this clarifies the tutorial