Analysis of discrete-time MAP/G/1 queue under workload control

In this paper, we analyze the discrete-time MAP/G/1 queue under the DD-policy in which the idle server resumes its service only when the accumulated workload exceeds the predetermined threshold DD. We first derive the probability generating functions of the queue length, workload, waiting time, and sojourn time distributions. Then we derive the mean performance measures. Lastly we present our numerical experience. Through the numerical examples we show the effects of the threshold and the variability of the service times on the mean performance measures, and the effect of the correlation between arrivals.