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2, (ii) explicit expressions for corresponding moments, and (iii) an explicit expression for the correlation between two buffer contents, again from the second buffer on. These results make use of a key observation concerning the aggregate contents of several consecutive buffers. For the case in which the active periods of the sources are exponential, the Laplace–Stieltjes transform is inverted. If there is only one source, all results are also valid for the first buffer.
doi:10.1016/j.peva.2007.06.022 
Copyright © 2007 Elsevier Ltd All rights reserved.
Heavy-tailed asymptotics for a fluid model driven by an M/G/1 queue
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Received 15 December 2004;
Abstract
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.
Keywords: Fluid queue; M/G/1 queue; Buffer content; Busy period; Regularly varying function
