Corpus ID: 119165045

# Finite-pool queues with heavy-tailed services

@article{Bet2016FinitepoolQW,
title={Finite-pool queues with heavy-tailed services},
author={G. Bet and R. Hofstad and J. V. Leeuwaarden},
journal={arXiv: Probability},
year={2016}
}
• Published 2016
• Mathematics
• arXiv: Probability
We consider the $\Delta_{(i)}/G/1$ queue, in which a a total of $n$ customers independently demand service after an exponential time. We focus on the case of heavy-tailed service times, and assume that the tail of the service time distribution decays like $x^{-\alpha}$, with $\alpha \in (1,2)$. We consider the asymptotic regime in which the population size grows to infinity and establish that the scaled queue length process converges to an \alpha-stable process with a negative quadratic drift… Expand
3 Citations

#### References

SHOWING 1-10 OF 23 REFERENCES
Asymptotic Analysis of the Time Dependent M/M/1 Queue
• W. Massey
• Mathematics, Computer Science
• Math. Oper. Res.
• 1985
Strong Approximations for Time-Dependent Queues
• Mathematics, Computer Science
• Math. Oper. Res.
• 1995
On Transitory Queueing
• Mathematics, Computer Science
• ArXiv
• 2014