Queueing Systems

, Volume 91, Issue 3–4, pp 319–346 | Cite as

Exact tail asymptotics for fluid models driven by an M/M/c queue

  • Wendi Li
  • Yuanyuan LiuEmail author
  • Yiqiang Q. Zhao


In this paper, we investigate exact tail asymptotics for the stationary distribution of a fluid model driven by the M / M / c queue, which is a two-dimensional queueing system with a discrete phase and a continuous level. We extend the kernel method to study tail asymptotics of its stationary distribution, and a total of three types of exact tail asymptotics are identified from our study and reported in the paper.


Fluid queue driven by an M / M / c queue Kernel method Exact tail asymptotics Stationary distribution Asymptotic analysis 

Mathematics Subject Classification

60K25 60J27 30E15 05A15 



This research was supported in part by the National Natural Science Foundation of China (Grants 11571372, 11771452), Natural Science Foundation of Hunan (Grant Nos. 2018JJ4357, 2017JJ2328), and a Discovery Grant by the Natural Sciences and Engineering Research Council of Canada (NSERC).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and Statistics, New CampusCentral South UniversityChangshaPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsCarleton UniversityOttawaCanada

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