Queueing Systems

, Volume 52, Issue 3, pp 193–198 | Cite as

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

  • Weixin Shang
  • Liming Liu
  • Quan-Lin Li


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.


M/G/1 retrial queue Queue length Subexponentiality Regular variation Tail asymptotics 


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© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Logistics ManagementHong Kong University of Science and TechnologyKowloonHong Kong
  2. 2.Department of Industrial EngineeringTsinghua UniversityBeijingP.R. China

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