# 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

#### 3 Citations

Finite-pool queueing with heavy-tailed services

- Computer Science, Mathematics
- Journal of Applied Probability
- 2017

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