The Annals of Probability
- Ann. Probab.
- Volume 2, Number 5 (1974), 815-827.
Cross-Spectral Analysis of Processes with Stationary Increments Including the Stationary $G/G/\infty$ Queue
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.
Ann. Probab., Volume 2, Number 5 (1974), 815-827.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F05: Central limit and other weak theorems
Secondary: 60K10: Applications (reliability, demand theory, etc.) 60K25: Queueing theory [See also 68M20, 90B22] 62M15: Spectral analysis
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