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}
}
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

Figures from this paper

Big jobs arrive early: From critical queues to random graphs
Rare events of transitory queues
  • Harsha Honnappa
  • Computer Science, Mathematics
  • Journal of Applied Probability
  • 2017

References

SHOWING 1-10 OF 23 REFERENCES
Queues with time-dependent arrival rates. III — A mild rush hour
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
An Introduction to Stochastic-Process Limits and their Application to Queues
  • W. Whitt
  • Computer Science, Mathematics
  • 2002
On Transitory Queueing
Large finite population queueing systems. The single-server model
Brownian excursions, critical random graphs and the multiplicative coalescent
The component sizes of a critical random graph with given degree sequence
Critical epidemics, random graphs, and Brownian motion with a parabolic drift
...
1
2
3
...