Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions (1997)
| Venue: | QUEUEING SYSTEMS |
| Citations: | 15 - 5 self |
BibTeX
@ARTICLE{Boxma97heavy-trafficanalysis,
author = {O.J. Boxma and J. W. Cohen},
title = {Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions},
journal = {QUEUEING SYSTEMS},
year = {1997},
volume = {33},
pages = {177--204}
}
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Abstract
We consider a GI/G/1 queue in which the service time distribution and/or the interarrival time distribution has a heavy tail, i.e., a tail behaviour like t \Gamma with 1 ! 2, so that the mean is finite but the variance is infinite. We prove a heavy-traffic limit theorem for the distribution of the stationary waiting time W. If the tail of the service time distribution is heavier than that of the interarrival time distribution, and the traffic load a ! 1, then W, multiplied by an appropriate `coefficient of contraction' that is a function of a, converges in distribution to the Kovalenko distribution. If the tail of the interarrival time distribution is heavier than that of the service time distribution, and the traffic load a ! 1, then W, multiplied by another appropriate `coefficient of contraction' that is a function of a, converges in distribution to the negative exponential distribution.
