In ATM networks, the purpose of connection admission control is to decide if allowing a nrw connection into the network violates a quality of service measure of the new connection or the existing connections. Instead of using statistical traffic models, we represent the connection entering the network by the connection traffic descriptors standardized by the ATM Forum and used by the connection admission control algorithms. In this paper, we examine traffic sources described by heterogeneous connection traffic descriptors in order to analyze constant bit rate sources versus variable bit rate sources, as well as different classes of variable bit rate sources. We use Monte Carlo simulation to estimate the cell loss probability of the combined traffic stream, as well as the individual classes using both random buffer filling and priority buffer filling schemes. Importance sampling is used to increase the efficiency of the simulation. For the experimental example considered here, the improvement in simulation efficiency compared to conventional Monte Carlo simulation is inversely proportional t o the estimate.'