Cross-Spectral Analysis of Processes with Stationary Increments Including the Stationary G/G/∞ 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/∞ 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/∞ 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.