Performance analysis and optimal control of the Geo/Geo/c queue

Discrete-time multiserver queues have been used for many years to investigate the behavior of communication and computer systems in which time is slotted. In this paper, we consider the discrete-time Geo/Geo/c queue. We first develop an efficient recursive procedure to obtain the steady-state probabilities and prove the convergence to the continuous-time counterpart. We also deal with the infinite-horizon discounted cost criterion for the arrival and service rate control problems. Optimal stationary policies and value functions are determined. This allows us to compare both control problems.