We study the behavior of large loss networks in which the offered
traffic is subject to acceptance controls. Hunt and Kurtz proved a functional
law of large numbers for the dynamics of such networks, as capacity and offered
traffic are allowed to increase in proportion. However, limiting dynamics were
not in general uniquely identified. We establish further results identifying
these dynamics under given conditions. We also investigate the existence of
fixed points for these dynamics and relate them to limiting equilibrium
behavior, permitting the investigation of common modelling assumptions. We
study in detail single- and two-resource networks and we give an example of
bistability for the former.
Publié le : 1997-11-14
Classification:
Loss network,
time-scale separation,
blocking probability,
60K30,
60F17,
60J27
@article{1043862415,
author = {Bean, N. G. and Gibbens, R. J. and Zachary, S.},
title = {Dynamic and equilibrium behavior of controlled loss
networks},
journal = {Ann. Appl. Probab.},
volume = {7},
number = {1},
year = {1997},
pages = { 873-885},
language = {en},
url = {http://dml.mathdoc.fr/item/1043862415}
}
Bean, N. G.; Gibbens, R. J.; Zachary, S. Dynamic and equilibrium behavior of controlled loss
networks. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp. 873-885. http://gdmltest.u-ga.fr/item/1043862415/