Analysis of discrete-time Geo/G/1 queue under the D-policy

In this paper, we present a theoretical and analytical framework to analyze the discrete-time queue in which the on-off of the server is controlled by workload threshold. For this purpose, we consider the discrete-time Geo/G/1 queue under the D-policy. We derive the queue length, waiting time, sojourn time distributions and the mean performance measures. We then perform numerical computations to see the effect of the threshold and the variability of the service time distributions on the system performance. We will also see if our discrete-time results can approximate the continuous-time M/G/1/D-policy queueing system. The approach of this paper can be used as a basis for the analysis of more complex queueing systems in which the server is controlled by workload.