Analysis of effective information transmission rate over fading channels has attracted much attentions in the last few years. Ergodic capacity and outage capacity, as two conventional indices, have been widely investigated in various scenarios. However, there exists a gap between them for any fixed average signal to noise ratio. Thus, one problem is raised naturally: How to fill this gap? To answer it, we shall propose a new concept, -overflow rate, which is used to characterize the transmission capability of a fading channel when a finite size buffer is employed at the transmitter. With this buffer, the constant rate source data stream is matched with the time varying channel status so that the fading channel can support a higher rate source data stream. It will be proved that the -overflow rate is larger than the -outage capacity under the same outage constraint and can converge to the ergodic capacity in all signal to noise ratio region.