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Methods for enhancing multistage interconnection network simulators running on massively parallel SIMD computers are presented. Aspects of parallel simulation of interconnection networks are discussed and different strategies of mapping the architecture of the network to be simulated onto the parallel machine are studied and compared. As case studies, two strategies of mapping synchronous multistage cube networks onto the MasPar MP-1 SIMD machine are explored and their implementations are compared. The methods result in an efficient simulator which can process 10^9 data packets in 40 minutes.