Big jobs arrive early: From critical queues to random graphs

@article{Bet2017BigJA,
  title={Big jobs arrive early: From critical queues to random graphs},
  author={G. Bet and R. Hofstad and J. V. Leeuwaarden},
  journal={arXiv: Probability},
  year={2017}
}
We consider a queue to which only a finite pool of $n$ customers can arrive, at times depending on their service requirement. A customer with stochastic service requirement $S$ arrives to the queue after an exponentially distributed time with mean $S^{-\alpha}$ for some $\alpha\in[0,1]$; so larger service requirements trigger customers to join earlier. This finite-pool queue interpolates between two previously studied cases: $\alpha = 0$ gives the so-called $\Delta_{(i)}/G/1$ queue and $\alpha… Expand
Finite-pool queueing with heavy-tailed services
Weighted Dyck paths for nonstationary queues

References

SHOWING 1-10 OF 27 REFERENCES
Finite-pool queues with heavy-tailed services
Heavy-Traffic Analysis Through Uniform Acceleration of Queues with Diminishing Populations
A queueing model with independent arrivals, and its fluid and diffusion limits
The component sizes of a critical random graph with given degree sequence
Heavy-tailed configuration models at criticality
The continuum limit of critical random graphs
Brownian excursions, critical random graphs and the multiplicative coalescent
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