We consider a storage model that can be either interpreted as a certain queueing model with dependence between a service request and the subsequent interarrival time, or as a fluid production/inventory model with a two-state random environment. We establish a direct link between the workload distributions of the queueing model and the production/inventory model, and we present a detailed analysis of the workload and waiting time process of the queueing system.
Boxma, O. J., & Perry, D. (2001). A queueing model with dependence between service and interarrival times. European Journal of Operational Research, 128(3), 611-624. https://doi.org/10.1016/S0377-2217(99)00396-3