In this paper, we give an overview on the Taylor expansion method developed in 1990s by Gong and Hu for the study of queueing systems, which have recently been found some new promising applications. We first use the GI/GI/1 queue to illustrate how the method works, then discuss how it can be applied to correlated queues, to analyzing the departure processes of queueing systems, and to developing high-order approximations for queueing networks. We also discuss several possible future research directions in this area.
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