Active intelligent reflecting surface (IRS) enables flexible signal reflection control with \emph{power amplification}, thus effectively compensating the product-distance path-loss in conventional passive-IRS aided systems. In this letter, we characterize the communication performance of an active-IRS aided single-cell wireless network. To this end, we first propose a \emph{customized} IRS deployment strategy, where the active IRSs are uniformly deployed within a ring concentric with the cell to serve the users far from the base station. Next, given the Nakagami-$m$ fading channel, we characterize the cascaded active-IRS channel by using the \emph{mixture Gamma distribution} approximation and derive a closed-form expression for the mean signal-to-noise ratio (SNR) at the user averaged over channel fading. Moreover, we numerically show that to maximize the system performance, it is necessary to choose a proper active-IRS density given a fixed number of total reflecting elements, which significantly differs from the passive-IRS case for which the centralized IRS deployment scheme is better. Furthermore, the active-IRS aided wireless network achieves higher spatial throughput than the passive-IRS counterpart when the total number of reflecting elements is small.