A compact model for the low and high resistance state conduction characteristics of electroformed capacitors with hexagonal boron nitride (A-BN) as insulator material and with multi-layer graphene and metal electrodes is presented. The model arises from an approximation of the expression for multi-filamentary electron transport with parabolic shaped constrictions. The model takes into account the parallel contribution of partially and fully formed localized current pathways spanning the two-dimensional (2D) film characterized by transmission coefficients T<;1 and T=1, respectively. It is shown how the resulting physical equation for a highly asymmetric constriction can be linked to an equivalent electrical circuit. The proposed approach unveils the connection between filamentary electron transport and diode-like conduction in resistive switching (RS) devices.