# 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…

## 18 Citations

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### Fork-join and redundancy systems with heavy-tailed job sizes

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Bounds are presented for the tail probability of the response time in the case of the first-come first-served (FCFS) discipline and it is indicated that having d = ⌈min{ ν ν−1, N − k}⌉ replicas is sufficient to achieve the optimal asymptotic tail behavior of theresponse time.

### Perfect simulation of M/G/c queues

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A perfect simulation algorithm for the stable M/G/c queue is described and a careful analysis shows that appropriate ordering relationships can still be maintained, so long as service durations continue to be coupled in order of initiation of service.

### Sample path large deviations for Lévy processes and random walks with Weibull increments

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