On Large Delays in Multi-Server Queues with Heavy Tails

@article{Foss2012OnLD,
  title={On Large Delays in Multi-Server Queues with Heavy Tails},
  author={Sergey Foss and Dmitry Korshunov},
  journal={Math. Oper. Res.},
  year={2012},
  volume={37},
  pages={201-218}
}
We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s first-come first-served (FCFS) queue. These bounds depend on the value of the traffic load ρ which is the ratio of mean service and mean interarrival times. For service times with intermediate regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a “principle of s-k big jumps” in this case (here k is the integer part of ρ), which… 

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