The fast progress in hardware technology for parallel computing has not always been accompanied by equivalent progress in software development, although in certain applications (matrix calculations, weather forecasts, ... ) a linear or even hyper-proportional speedup with respect to the number of processors has been demonstrated. At first sight, the simulation of complex communication networks with its many concurrent activities seems to be well suited for parallel computing. In the 70s first proposals on extending the principles of discrete event simulation to distributed simulation have been made. Since then research focussed on the study of clock control mechanisms for closely and loosely coupled parallel systems. Recently a parallel simulator employing a special clock synchronization has been built where the synchronization mechanism 'time warp' is embedded in a dedicated integrated circuit. The emerging broadband communication networks based on the asynchronous transfer mode (ATM) pose new challenges on simulation techniques. There are different control mechanisms working at different timescales to be covered in one simulation model and, also, cell losses as rare events to be investigated. This contribution begins with an overview of the evolution of distributed simulation techniques for discrete event systems. It discusses at which modelling level a parallelization of simulation tasks is possible. Then the typical behaviour of broadband subscribers with a variable bitrate is presented. Finally we discuss the feasibility of the presented simulation techniques to study the hard requirements for the quality of service in ATM networks.