ON APPROXIMATIONS FOR THE GI GI 1 QUEUE

This paper contains a investigation of mean waiting time (and queue length) approximations for the GI/GI/1 queue. A great number of previous works on the subject have appeared. An important background for the present work is an ITC-paper by Sudhofen and Pawlita, containing a study of the H2/M/1 queue. This queue has a well-known solution. In the present work it is pointed out that two extremes of the third moment of the H2 distribution correspond to batch Poisson and pure Poisson. Those arrival cases have known solutions for general service distributions, i.e. the M(B)/GI/1 case and the M/GI/1 case. This fact is used to construct a new approximation for the GI/GI/1 queue, based on an interpolation between the two known extremes. The new approximation is compared with a set of previously published approximations through calculations and simulations for a broad range of distribution parameters.