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Abstract-This paper introduces a queueing analysis of a two-tier service supercomputer system, where one type of processors offers service with a finite waiting buffer and the other offers unlimited waiting buffer. From the managerial viewpoint of system, a two-tier queueing model is developed to investigate the dynamic performance of the supercomputer system under finite buffer control. The queueing system is formulated as a state dependent quasi-birth-and-death (QBD) process with twodimensional state space. System performance measures can be obtained through the matrix geometric solution for such a QBD process.