In this paper, we derive the MacLaurin series of the mean waiting time in light traffic 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 Padé approximation.

We consider a class of G/G/1 queueing models with independent generalized setup time and exhaustive service. It is shown that a variety of single-server queueing systems with service interruption are special cases of our model. We give a simple computational scheme for the moments of the stationary waiting time and sojourn time. Our numerical investigations indicate that the algorithm is quite accurate and fast in general. For the M/G/1 case, we are able to derive a recursive formula for the moments of the stationary waiting time, which includes the Takács formula as a special case. It immediately results in the stochastic decompòsition property which can be found in the literature.