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This paper presents an analysis of the departure process of a discrete-time Geo/G/1 queuewith randomized vacations. By using probability decomposition techniques and renewal process, theexpression of expected number of departures during time interval (0+,n+] is derived. The relationamong departure process, server state process, and service renewal process is obtained. The relationdisplays the decomposition characteristic of the departure process. Furthermore, the approximateexpansion of the expected number of departures is gained. Since the departure process also oftencorresponds to an arrival process for a downstream queue in queueing network, it is hoped that theresults obtained in this paper may provide useful information for queueing network

discrete dynamics in nature and society

Study on the Departure Process of Discrete-Time<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>Geo</mml:mi></mml:mrow></mml:math>/<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>/<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>1</mml:mi></mml:mrow></mml:math>Queue with Randomized Vacations

Study on the Departure Process of Discrete-TimeGeo/G/1Queue with Randomized Vacations