# The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution

@article{Whitt2000TheIO,
title={The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution},
author={Ward Whitt},
journal={Queueing Systems},
year={2000},
volume={36},
pages={71-87}
}
• W. Whitt
• Published 14 November 2000
• Mathematics
• Queueing Systems
By exploiting an infinite-server-model lower bound, we show that the tails of the steady-state and transient waiting-time distributions in the M/GI/s queue with unlimited waiting room and the first-come first-served discipline are bounded below by tails of Poisson distributions. As a consequence, the tail of the steady-state waiting-time distribution is bounded below by a constant times the sth power of the tail of the service-time stationary-excess distribution. We apply that bound to show…

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