Mean Waiting Time of a GI/G/1 Queue in Light Traffic Via Random Thinning

摘要

In this paper, we derive the MacLaurin series of the mean waiting time in lighttraffic for a GI/G/1 queue, The light traffic is defined by random thinning of the arrival process. The MacLaurin series is derived with respect to the admission probability, and we prove that it has a positive radius of convergence. In the numerical examples, we use the MacLaurin series to approximate the mean waiting time beyond light traffic by means of Pade approximation.