We consider a symmetric network composed of $N$ links, each with
capacity $C$. Calls arrive according to a Poisson process, and each call
concerns $L$ distinct links chosen uniformly at random. If each of these
links has free capacity, the call is held for an exponential time; otherwise it
is lost. The semiexplicit stationary distribution for this process is similar
to a Gibbs measure: it involves a normalizing factor, the partition function,
which is very difficult to evaluate.We let $N$ go to infinity and keep
fixed the rate of call attempts concerning any link. We use asymptotic
combinatorics and recent techniques involving the law of large numbers to
obtain the asymptotic equivalent for the logarithm of the partition function
and then the large deviation principle for the empirical measure of the
occupancies of the links. We give an explicit formula for the rate function and
examine its properties.
Publié le : 2000-02-14
Classification:
Large networkds,
stationary distribution,
partition function,
large deviations.,
60F10,
60K35,
60G10,
68M10,
90B12
@article{1019737666,
author = {Graham, Carl and O'Connell, Neil},
title = {Large deviations at equilibrium for a large star-shaped loss
network},
journal = {Ann. Appl. Probab.},
volume = {10},
number = {2},
year = {2000},
pages = { 104-122},
language = {en},
url = {http://dml.mathdoc.fr/item/1019737666}
}
Graham, Carl; O'Connell, Neil. Large deviations at equilibrium for a large star-shaped loss
network. Ann. Appl. Probab., Tome 10 (2000) no. 2, pp. 104-122. http://gdmltest.u-ga.fr/item/1019737666/