Heavy-Traffic Analysis Through Uniform Acceleration of Queues with Diminishing Populations

@article{Bet2019HeavyTrafficAT,
  title={Heavy-Traffic Analysis Through Uniform Acceleration of Queues with Diminishing Populations},
  author={G. Bet and R. Hofstad and J. V. Leeuwaarden},
  journal={Math. Oper. Res.},
  year={2019},
  volume={44},
  pages={821-864}
}
We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic behavior by using uniform acceleration, which simultaneously lets $n$ and the service rate grow large, while the initial resource utilization approaches one. A key feature of the model is that, as time progresses, more customers have joined the queue, and… Expand
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