This paper treats transience for queueing network models by considering an associated fluid limit model. If starting from any initial condition the fluid limit model explodes at a linear rate, then the associated queueing network with i.i.d. service times and a renewal arrival process explodes faster than any fractional power.
@article{1177004601,
author = {Meyn, Sean P.},
title = {Transience of Multiclass Queueing Networks Via Fluid Limit Models},
journal = {Ann. Appl. Probab.},
volume = {5},
number = {4},
year = {1995},
pages = { 946-957},
language = {en},
url = {http://dml.mathdoc.fr/item/1177004601}
}
Meyn, Sean P. Transience of Multiclass Queueing Networks Via Fluid Limit Models. Ann. Appl. Probab., Tome 5 (1995) no. 4, pp. 946-957. http://gdmltest.u-ga.fr/item/1177004601/