We consider a network in which a call holds a given number of uniformly chosen links and releases them simultaneously. We show pathwise propagation of chaos and convergence of the process of empirical fluctuations to a Gaussian Ornstein-Uhlenbeck process. The limiting martingale problem is obtained by closing a hierarchy. The drift term is given by a simple factorization technique related to mean-field interaction, but the Doob-Meyer bracket contains special terms coming from the strong interaction due to simultaneous release. This is treated by closing another hierarchy pertaining to a measure-valued process related to calls routed through couples of links, and the factorization is again related to mean-field interaction. Fine estimates obtained by pathwise interaction graph constructions are used for tightness purposes and are thus shown to be of optimal order.
Publié le : 1995-08-14
Classification:
Networks,
interaction graphs,
hierarchies,
propagation of chaos,
fluctuations,
60K35,
60F05,
60F17,
68M10,
90B12
@article{1177004700,
author = {Graham, Carl and Meleard, Sylvie},
title = {Dynamic Asymptotic Results for a Generalized Star-Shaped Loss Network},
journal = {Ann. Appl. Probab.},
volume = {5},
number = {4},
year = {1995},
pages = { 666-680},
language = {en},
url = {http://dml.mathdoc.fr/item/1177004700}
}
Graham, Carl; Meleard, Sylvie. Dynamic Asymptotic Results for a Generalized Star-Shaped Loss Network. Ann. Appl. Probab., Tome 5 (1995) no. 4, pp. 666-680. http://gdmltest.u-ga.fr/item/1177004700/