Large Deviation Analysis of Subexponential Waiting Times in a Processor-Sharing Queue

@article{Jelenkovic2003LargeDA,
  title={Large Deviation Analysis of Subexponential Waiting Times in a Processor-Sharing Queue},
  author={Predrag R. Jelenkovic and Petar Momcilovic},
  journal={Math. Oper. Res.},
  year={2003},
  volume={28},
  pages={587-608}
}
We investigate the distribution of the waiting time V in a stable M/G/1 processor sharing queue with traÆc intensity < 1. When the distribution of a customer service request B belongs to a large class of subexponential distributions with tails heavier than e p x, it is shown that P[V > x] = P[B > (1 )x](1 + o(1)) as x!1: Furthermore, we demonstrate that the preceding relationship does not hold if the service distribution has a lighter tail than e p x. 
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References

Publications referenced by this paper.
Showing 1-10 of 24 references

Bandwidth Sharing: Objectives and Algorithms

View 6 Excerpts
Highly Influenced

Applied Probability and Queues

S. 73–89. Asmussen
1987
View 5 Excerpts
Highly Influenced

Integral limit theorems taking large deviations into account when Cramér’s condition

A. V. 152–167. Nagaev
1969
View 5 Excerpts
Highly Influenced

Sojourn time asymptotics in the MG1 processor sharing queue

Queueing Syst. • 2000
View 3 Excerpts
Highly Influenced

On the tails of waiting-time distribution

A. G. 360–378. Pakes
J. Appl. Probab • 1975
View 2 Excerpts
Highly Influenced

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