In this letter, we present a channel access strategy with both downward and upward (thus called both-way) overflow mechanisms, which allocates channel bandwidth dynamically to multiple heterogeneous traffics with differing intensities, bit rates and holding times. Each input traffic has its own service channel and finite waiting room and can overflow to any other channels. The threshold parameter which limits overflow is also considered, and the performance of this channel access strategy is analyzed as an M/M/S/N system with state-dependent arrival rates.