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We develop a simulation model of the OSI network layer of packet-switching networks. We present the scope of our research and the need for simulation tools. We discuss the migration from an MS Windows interactive, real-time, GUI-based tool to two packages that can run under Linux. We describe aspects common to all serial execution versions that have been extensively used in a serial execution under the SHARCNET environment. Then, we focus on the porting to a parallel implementation. We examine and discuss alternate candidate solutions and their trade-offs while converting the serial code to the parallel code. We discuss the parallelization of the code using pthread POSIX threading. Current work is targeted to design a model with a parallel architecture in mind from the outset.