Tail Asymptotics for M/G/1 Type Queueing Processes with Subexponential Increments

@article{Asmussen1999TailAF,
  title={Tail Asymptotics for M/G/1 Type Queueing Processes with Subexponential Increments},
  author={S\oren Asmussen and Jakob R. M\oller},
  journal={Queueing Syst.},
  year={1999},
  volume={33},
  pages={153-176}
}
Bivariate regenerative Markov modulated queueing processes {In,Ln} are described. {In} is the phase process, and {Ln} is the level process. Increments in the level process have subexponential distributions. A general boundary behavior at the level 0 is allowed. The asymptotic tail of the cycle maximum, MCreg , during a regenerative cycle, C, and the asymptotic tail of the stationary random variable L∞, respectively, of the level process are given and shown to be subexponential with L∞ having… CONTINUE READING

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