We consider a time-slotted queueing model where each time slot can either be an arrival slot, in which new packets arrive, or a departure slot, in which packets are transmitted and hence depart from the queue. The slot scheduling strategy we consider describes periodically, and for a fixed number of time slots, which slots are arrival and departure slots. We consider a static and a dynamic strategy. For both strategies, we obtain expressions for the probability generating function of the steady-state queue length and the packet delay. The model is motivated by cable-access networks, which are often regulated by a request–grant procedure in which actual data transmission is preceded by a reservation procedure. Time slots can then either be used for reservation or for data transmission.
Leeuwaarden, van, J. S. H., Denteneer, T. J. J., & Resing, J. A. C. (2006). A discrete-time queueing model with periodically scheduled arrival and departure slots. Performance Evaluation, 63(4-5), 278-294. https://doi.org/10.1016/j.peva.2005.03.001