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In this article and as a generalization to our work in Fayza et al. (2003), we present a case study of ATM buffers with batch arrivals, geometric service time and priority scheduling. Packets belongs to two classes, class-1 packets represents real time traffics which is delay sensitive but loss insensitive, and class-2 packets represents non real time traffics which is delay insensitive but loss sensitive. Higher service priority is given to real time traffics (audio and video) to respond to the delay sensitivity in the presence of multiple servers in the system. Expressions for the expected values of the main performance measures of the system are evaluated. Some numerical examples are presented to illustrate the significance of using priority scheduling and a multiserver system.