The authors study the loss performance of an asynchronous transfer mode (ATM) multiplexer, whose input consists of the superposition of a multiplicity of heterogeneous on-off sources. The stochastic fluid flow approach yields the entire buffer occupancy probability distribution in terms of the solution of a linear differential equation system. The focus is on the numerical investigation of the steady-state behavior of models involving very large state spaces. A novel approximate technique is introduced allowing a dramatic reduction of the computational burden, so that the analysis of a large variety of traffic mixes becomes feasible. Many numerical results are presented to support the accuracy of the method. Applications of the analysis method are outlined.>