Simple and explicit bounds for multi-server queues with universal 1 1 − ρ ( and better ) scaling

@inproceedings{Li2017SimpleAE,
  title={Simple and explicit bounds for multi-server queues with universal 1 1 − ρ ( and better ) scaling},
  author={Yuan Li and David Alan Goldberg},
  year={2017}
}
We consider the FCFS GI/GI/n queue, and prove the first simple and explicit bounds that scale gracefully and universally as 1 1−ρ (and better), with ρ the corresponding traffic intensity. In particular, we prove the first multi-server analogue of Kingman’s bound, which has been an open problem for over fifty years. Our main results are bounds for the tail of the steady-state queue length and the steady-state probability of delay, where the strength of our bounds (e.g. in the form of tail decay… CONTINUE READING

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