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A GI/G/1 queueing system with finite capacity il studied. The first overflow time, which means the time when the number of customers first exceeds the capacity, is analyzed by diffusion approximation. Approximate expressions for the distribution and moments of the first overflow time are derived explicitly. These results are modified so as to be more accurate for an M/G/I system or a system with small capacity. Further these results are applied to the analysis of the maximum number of customers up to time t in a GI/G/I system with infinite capacity. Finally, the accuracy of the diffusion approximations is examined numerieally by using the analytical results for a GI/M/I system.

DIFFUSION APPROXIMATION FOR GI/G/1 QUEUING SYSTEMS WITH FINITE CAPACITY : I-THE FIRST OVERFLOW TIME