INTERPOLATION APPROXIMATIONS FOR THE MEAN WAITING TIME IN A MULTISERVER QUEUE

This paper gives numerical validation of a couple of interpolation approximation, fr the mean waiting time in a GI/G/s queue, which are provided by a unified approach similar to that in Kimura (1991). Both approximations are represented as certain combinations of the mean waiting times for the GI/M/s and GI/D/s queues in which the arrival processes and the mean service times are the same as in the approximating GI/G/s queue. To let these approximations be more tractable, we further provide simple interpolation approximations for the mean waiting times in GI/M/s and GI/D/s queues with low variable interarrival times. The quality of the approximations is tested by comparing them with exact solutions and previous two-moment approximations for a variety of cases. Extensive numerical comparisons indicate thal our approximations are more accurate than the two-moment approximations and that the relative percentage errors are in the order of 5% in moderate traffic and in the order of 1% in heavy traffic.