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October, 1974 Cross-Spectral Analysis of Processes with Stationary Increments Including the Stationary $G/G/\infty$ Queue
David R. Brillinger
Ann. Probab. 2(5): 815-827 (October, 1974). DOI: 10.1214/aop/1176996550


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.


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David R. Brillinger. "Cross-Spectral Analysis of Processes with Stationary Increments Including the Stationary $G/G/\infty$ Queue." Ann. Probab. 2 (5) 815 - 827, October, 1974.


Published: October, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0292.60063
MathSciNet: MR359221
Digital Object Identifier: 10.1214/aop/1176996550

Primary: 60F05
Secondary: 60K10 , 60K25 , 62M15

Keywords: point process , queue , spectral analysis , system identification

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 5 • October, 1974
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