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Assessment, computation and establishment of methods for decreasing communication overheads in parallel computing systems using multi-processor architectures are important problems. In the current research, the communication overhead was assessed using a new method that was executed based on components such as: effectiveness of the interconnecting network architecture, delay of nodes, initial communication time and transferring time of one data. The effectiveness of the communication overhead in the parallel computing system was also analyzed using the closed product form queueing network.