We consider a linear time invariant model relating one process with stationary increments to another such process. The model contains the stationary $G/G/\infty$ queue and a bivariate cluster process as particular cases. The parameters of the model are shown to be identifiable through cross-spectral analysis and estimates are shown to be asymptotically normal under regularity conditions. In the case of the $G/G/\infty$ queue, the parameters considered are the characteristic function and the distribution function of the service time. The estimates are based on a stretch of entry and exit times for the system.
Publié le : 1974-10-14
Classification:
Spectral analysis,
point process,
queue,
system identification,
60F05,
60K10,
60K25,
62M15
@article{1176996550,
author = {Brillinger, David R.},
title = {Cross-Spectral Analysis of Processes with Stationary Increments Including the Stationary $G/G/\infty$ Queue},
journal = {Ann. Probab.},
volume = {2},
number = {6},
year = {1974},
pages = { 815-827},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996550}
}
Brillinger, David R. Cross-Spectral Analysis of Processes with Stationary Increments Including the Stationary $G/G/\infty$ Queue. Ann. Probab., Tome 2 (1974) no. 6, pp. 815-827. http://gdmltest.u-ga.fr/item/1176996550/