Chuan Yi LUO, Ying Hui TANG, Bao Shan CAO, Kai Li XIANG
We study the departure process of a multi-vacation Geo/G/1 queue with variable input rate. Using probability techniques, renewal process theory and utransform, we discuss the expected number of departures during the time interval (0+,n+] initiated with general state. The decomposed expression of the expected number of departures during the time interval (0+,n+] and the corresponding steady result are obtained. It displays the especial structure of the departure renewal process, i.e., the departure renewal process consists of two parts, server busy-state process (busy or idle) and the service renewal process in server busy period, which simplifies the discussion on the departure renewal process. Since the departure process also often corresponds to an arrival process in downstream queues, the results obtained here are significant to study queueing network.