Evaluating the Overflow Probability Using the Infinite Queue

This paper presents an approximation formula for the overflow probability for GI/GI/c(N) queues in terms of a queue-length distribution for the corresponding GI/GI/c(∞) queues, where N is the total capacity of the system. The approximation is based on the conservation law, and on assumptions which might be acceptable if N ≫ c. The authors' approximation formula is numerically examined for various phase-type GI/GI/c(N) queues and the results show that the approximation is very good for practical parameter settings. The authors' approximation stands merely on a stationarity assumption. Therefore, it is also expected to be good for G/G/c(N) queues with a large N.