# 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

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