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