We consider a broadcast scenario where one transmitter communicates with two receivers under quality-of-service constraints. The transmitter initially employs superposition coding strategies with arbitrarily distributed signals and sends data to both receivers. Regarding the channel state conditions, the receivers perform successive interference cancellation to decode their own data. We express the effective capacity region that provides the maximum allowable sustainable data arrival rate region at the transmitter buffer or buffers. Given an average transmission power limit, we provide a two-step approach to obtain the optimal power allocation policies that maximize the effective capacity region. Then, we characterize the optimal decoding regions at the receivers in the space spanned by the channel fading power values. We finally substantiate our results with numerical presentations.