Three-moment approximation for the mean queue time of a GI/G/1 queue

The approximation of a GI/G/1 queue plays a key role in the performance evaluation of queueing systems. To improve the conventional two-moment approximations, we propose a three-moment approximation for the mean queue time of a GI/G/1 queue based on the exact results of the H₂/M/1 queue. The model is validated over a wide range of numerical experiments. Based on paired t-tests, our three-moment approximation outperforms the two-moment ones when the inter-arrival time variability is greater than one.