Tail asymptotics for the queue length in an M/G/1 retrial queue

Authors:
Weixin Shang;Liming Liu;Quan-Lin Li
Affiliations:
Department of Industrial Engineering and Logistics Management, Hong Kong University of Science and Technology, Kowloon, Hong Kong;Department of Industrial Engineering and Logistics Management, Hong Kong University of Science and Technology, Kowloon, Hong Kong;Department of Industrial Engineering, Tsinghua University, Beijing, P.R. China 100084
Venue:
Queueing Systems: Theory and Applications
Year:
2006

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Abstract

In this paper, we study the tail behavior of the stationary queue length of an M/G/1 retrial queue. We show that the subexponential tail of the stationary queue length of an M/G/1 retrial queue is determined by that of the corresponding M/G/1 queue, and hence the stationary queue length in an M/G/1 retrial queue is subexponential if the stationary queue length in the corresponding M/G/1 queue is subexponential. Our results for subexponential tails also apply to regularly varying tails, and we provide the regularly varying tail asymptotics for the stationary queue length of the M/G/1 retrial queue.