This report examines some of the issues arising m the implementation of statistical multiplexing in a broadband Integrated digital services network (B-ISDN) by analysis and simulation The BISDN concept is introduced and described. A review o f the current areas of research is given along with some of the important issues as they relate to telephone traffic. The report then focuses on the problem o f multiplexing voice traffic. A typical voice source is analysed and the traffic characteristics which result are described. The concept of statistical multiplexing is mtroduced. A review of the current literature studies relating to the problems of analysing multiplexed sources is given, with particular reference to the concept of cell level and burst level queues being separate and disparate components requiring different analytical approaches. Several models are mtroduced including the 3-state model not previously described in the literature. The queue behaviour resulting from a large number of superposed lmes is analysed as a simplified Markov process and the results are used to argue that it is not feasible to provide buffers for nodes which multiplex a large number of low intensity sources. The problem of scaling small models up to realistic situations is discussed. An approach to simulating the problem is described along with algorithms for implementing the basic elements. A senes of results derived from the described simulation are presented and analysed. The report concludes that statistical multiplexing is feasible, but with certain limits as to the type of traffic which can be supported.