Heavy-tailed asymptotics for a fluid model driven by an queue

In this paper, an infinite-buffer fluid queue driven by an M / G / 1 queue is discussed. The Laplace transform of the distribution of the stationary buffer content is expressed through the minimal positive solution to a crucial equation, similar to the fundamental equation satisfied by the busy period of an M / G / 1 queue. Furthermore, the distribution of the stationary buffer content is shown to be regularly varying with index − α + 1 if the distribution of the service times is regularly varying with index − α < − 1 . Meanwhile, the first ⌈ α ⌉ − 2 moments of the stationary buffer content are given, where ⌈ x ⌉ is the ceiling function of the real number x .