Exponential bounds for queues with Markovian arrivals

@article{Duffield1994ExponentialBF,
  title={Exponential bounds for queues with Markovian arrivals},
  author={Nick G. Duffield},
  journal={Queueing Syst.},
  year={1994},
  volume={17},
  pages={413-430}
}
Exponential bounds P[queue > b] < ~e -'rb are found for queues whose increments are described by Markov Additive Processes. This is done by application of maximal inequalities to exponential martingales for such processes. Through a thermodynamic approach the constant ,~ is shown to be the decay rate for an asymptotic lower bound for the queue length distribution. The class of arrival processes considered includes a wide variety of Markovian multiplexer models, and a general treatment of these… CONTINUE READING
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