Heavy-tailed asymptotics for a fluid model driven by an M/G/1 queue

Authors:
Quan-Lin Li;Liming Liu;Weixin Shang
Affiliations:
Department of Industrial Engineering, Tsinghua University, Beijing 100084, China;Faculty of Business, Hong Kong Polytechnic University, Hung Hom, Hong Kong;School of Management, Fudan University, Shanghai 200433, China
Venue:
Performance Evaluation
Year:
2008

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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 -@a+1 if the distribution of the service times is regularly varying with index -@a