Heavy-tailed asymptotics for a fluid model driven by an M/G/1 queue
Fluid queue, M/G/1, queue, Buffer content, Busy period, Regularly varying function
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
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Li, Q.-L., Liu, L., & Shang, W. (2008). Heavy-tailed asymptotics for a fluid model driven by an M/G/1 queue. Performance Evaluation, 65(3-4), 227-240. doi: 10.1016/j.peva.2007.06.022