This paper investigates the effect of various operation parameters on the downlink user performance in overlaid small-cell networks. The case study considers closed-access small cells (e.g., femtocells), wherein only active authorized user equipments (UEs) can be served, and each of which is allocated single downlink channel at a time. On the other hand, the macrocell base station can unconditionally serve macrocell UEs that exist inside its coverage space. The available channels can be shared simultaneously in the macrocell network and the femtocell network. Moreover, a channel can be reused only at the macrocell base station. The analysis provides quantitative approaches to model UEs identities, their likelihoods of being active, and their likelihoods of producing interference, considering UEs classifications, locations, and access capabilities. Moreover, it develops models for various interference sources observed from effective interference femtocells, considering femtocells capacities and operation conditions. The associated formulations to describe a desired UE performance and the impact of the number of available channels as well as the adopted channel assignment approach are thoroughly investigated. The results are generally presented for any channel models of interference sources as well as the desired source of the served UE. Moreover, specific channel models are then adopted, for which generalized closedform analytical results for the desired UE outage probability performance are obtained. Numerical and simulation results are presented to further clarify the main outcomes of the developed analysis.