With the emerging of broadband networks based on ATM technology, performance evaluation tools that allow the study of large systems are desperately needed. We present our experiments in distributed simulation of large and complex ATM network models with a conservative simulator. The goal here was not to achieve the maximum speedup with well shaped topologies bat rather to see what speedup can be obtained with a realistic model on a "state of the art" parallel computer. A network model with 78 switches is simulated on a Cray T3E using 3 different traffic loads. The performance results show that good speedups can be achieved but they also highlight partitioning problems and bottlenecks in the simulation model that can seriously limit the speedup of realistic model simulations.