We study the time it takes until a fluid queue with a finite, but
large, holding capacity reaches the overflow point. The queue is fed by an
on/off process with a heavy tailed on distribution which is known
to have long memory. It turns out that the expected time until overflow, as a
function of capacity L, increases only polynomially fast; so overflows
happen much more often than in the "classical" light tailed case, where the
expected over-flow time increases as an exponential function of L.
Moreover, we show that in the heavy tailed case overflows are basically caused
by single huge jobs. An implication is that the usual $GI/G/1$ queue with
finite but large holding capacity and heavy tailed service times will overflow
about equally often no matter how much we increase the service rate. We
also study the time until overflow for queues fed by a superposition of
k iid on/off processes with a heavy tailed on
distribution, and we show the benefit of pooling the system resources as far as
time until overflow is concerned.
Publié le : 1997-11-14
Classification:
Long range dependence,
heavy tails,
on/off models,
$G/G/1$ queue,
fluid models,
long memory,
heavy tailed distribution,
regular variation,
time to hit a level,
buffer overflow,
maximum work load,
weak convergence,
60K25,
90B15
@article{1043862423,
author = {Heath, David and Resnick, Sidney and Samorodnitsky, Gennady},
title = {Patterns of buffer overflow in a class of queues with long memory
in the input stream},
journal = {Ann. Appl. Probab.},
volume = {7},
number = {1},
year = {1997},
pages = { 1021-1057},
language = {en},
url = {http://dml.mathdoc.fr/item/1043862423}
}
Heath, David; Resnick, Sidney; Samorodnitsky, Gennady. Patterns of buffer overflow in a class of queues with long memory
in the input stream. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp. 1021-1057. http://gdmltest.u-ga.fr/item/1043862423/