Study on the Departure Process of Discrete-Time // Queue with Randomized Vacations

This paper presents an analysis of the departure process of a discrete-time queue with randomized vacations. By using probability decomposition techniques and renewal process, the expression of expected number of departures during time interval is derived. The relation among departure process, server state process, and service renewal process is obtained. The relation displays the decomposition characteristic of the departure process. Furthermore, the approximate expansion of the expected number of departures is gained. Since the departure process also often corresponds to an arrival process for a downstream queue in queueing network, it is hoped that the results obtained in this paper may provide useful information for queueing network.

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