## The Annals of Probability

### Cross-Spectral Analysis of Processes with Stationary Increments Including the Stationary $G/G/\infty$ Queue

David R. Brillinger

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 2, Number 5 (1974), 815-827.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996550

Digital Object Identifier
doi:10.1214/aop/1176996550

Mathematical Reviews number (MathSciNet)
MR359221

Zentralblatt MATH identifier
0292.60063

JSTOR
Brillinger, David R. Cross-Spectral Analysis of Processes with Stationary Increments Including the Stationary $G/G/\infty$ Queue. Ann. Probab. 2 (1974), no. 5, 815--827. doi:10.1214/aop/1176996550. https://projecteuclid.org/euclid.aop/1176996550