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In this research, the performance evaluation of two class priority Delta Multistage Interconnection Networks (MINs) is analyzed, using a discrete priority queuing model. All Delta Networks are constructed by special switching elements (SEs) based on an architecture which natively supports two classes of routing traffic. The proposed analytical method which was developed for performance metrics investigation can be applied on any class of Banyan Switches, because the model is independent from their internal link permutations, providing results for all intermediate stages. The analytical method was validated by simulation experiments and the obtained results in the marginal cases of single priority MINs were found to be more accurate as compared with those of three older classic models.The proposed architecture of Delta Networks which have been thoroughly analyzed by our analytical model can be useful in the study and development of communication links that support both voice and data traffic co instantaneously, with good quality of service.