This paper applies the earlier work of Barlow, Rogers and Williams on the Wiener-Hopf factorization of finite Markov chains to a number of questions in the theory of fluid models of queues. Specifically, the invariant distribution for an infinite-buffer model and for a finite-buffer model are derived. The laws of other functionals of the fluid models can be easily derived and compactly expressed in terms of the fundamental Wiener-Hopf factorization.
@article{1177005065,
author = {Rogers, L. C. G.},
title = {Fluid Models in Queueing Theory and Wiener-Hopf Factorization of Markov Chains},
journal = {Ann. Appl. Probab.},
volume = {4},
number = {4},
year = {1994},
pages = { 390-413},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005065}
}
Rogers, L. C. G. Fluid Models in Queueing Theory and Wiener-Hopf Factorization of Markov Chains. Ann. Appl. Probab., Tome 4 (1994) no. 4, pp. 390-413. http://gdmltest.u-ga.fr/item/1177005065/