At a buffered switch in anATM (asynchronous transfer mode) network it is important to know what combinations of different types of traffc can be carried simultaneously without risking more than a very small probability of overflowing the buffer. We argue that for many stationary sources an effective bandwidth is given by a formula involving just the source mean rate, its index of dispersion and the size of the buffer. We report computational experiments that support the practicality of this formula.