Overflows occur in finite capacity queuing systems such as M/G/1/K, and M/G/1/K/N. The exact mean time to the first overflow from a start of the system is derived in Takagi (1993), for the models with system capacity 1 (K=1). Not much works have been done when the system capacity is larger than 1. Will be shown that an approximation can be obtained in this case, that is, for M/G/1/K/n, which is a general model with system capacity larger than 1.

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