At a buffered switch in a asynchronous transfer mode network it is important to know what combinations of different classes of traffic can be carried simultaneously without risking more than a very small proportion of cells being lost by overflows of the buffer. The paper explains an algorithm for estimating the cell loss rate from a special on-line simulation and also how effective bandwidths may be computer for certain stationary traffic sources. For large buffers the effective bandwidth of a source is a function only of its mean rate, index of dispersion and the size of the buffer.