Queueing Systems

, Volume 91, Issue 3–4, pp 319–346

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

• Wendi Li
• Yuanyuan Liu
• Yiqiang Q. Zhao
Article

## Abstract

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.

## Keywords

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

## Notes

### Acknowledgements

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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