This paper analyzes a discrete-time Geoa/Geob/1 queuing system with batch
arrivals of fixed size a , and batch services of fixed size b. Both arrivals and services
occur randomly following a geometric distribution. The steady-state
queue length distribution is obtained as the solution of a system of difference
equations. Necessary and sufficient conditions are given for the system to be
stationary. Besides, the uniqueness of the root of the characteristic polynomial
in the interval (0, 1) is proven which is the only root needed for the computation
of the theoretical solution with the proposed procedure. The theoretical
results are compared with the ones observed in some simulations of the
queuing system under different sets of parameters. The agreement of the results
encourages the use of simulation for more complex systems. Finally, we
explore the effect of parameters on the mean length of the queue as well as on
the mean waiting time.
