A theoretical conduction model for structures composed of a number of conducting islands that are coupled to each other, and to external leads/gates via tunnel junctions has been developed. In this semiclassical approach, each tunnel junction is modeled by a tunneling resistance,R, and a tunnel capacitance,C. Extending the work of Ammanet al., from the case of two mesoscopic tunnel junctions coupled in series to more general structures composed of more than a single island, we find that a detailed balance of tunneling rates remains valid. However, for a multiple island system, a detailed balance of tunneling rates does not imply a detailed balance of occupation probabilities under steady state conditions. A universally applicable master equation for the occupation probability has been derived. Without the aid of detailed balance it is not possible to obtain closed form solutions for the occupation probability; therefore, an iterative method was implemented to solve the master equation for the multivariate occupation probability density function. Currently, this method can be utilized in calculating both the Coulomb staircase behavior of current(s) versus bias voltage(s), and the Coulomb oscillations of conductance versus gate voltages.
