Analysis of the GI/Geo/1 queue with N-policy |
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| Authors: | Dae-Eun Lim Doo Ho Lee Won Seok Yang Kyung-Chul Chae |
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| Institution: | 1. Division of Business and Commerce, Baekseok University, Chungnam 330–704, South Korea;2. Big Data Software Research Laboratory, ETRI, Daejeon, 305–700, South Korea;3. Department of Business Administration, Hannam University, Daejeon 306–791, South Korea;4. Department of Industrial and Systems Engineering, KAIST, Daejeon, 305–701, South Korea |
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| Abstract: | We consider a discrete-time single server N -policy GI/Geo/1 queueing system. The server stops servicing whenever the system becomes empty, and resumes its service as soon as the number of waiting customers in the queue reaches N. Using an embedded Markov chain and a trial solution approach, the stationary queue length distribution at arrival epochs is obtained. Furthermore, we obtain the stationary queue length distribution at arbitrary epochs by using the preceding result and a semi-Markov process. The sojourn time distribution is also presented. |
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| Keywords: | Discrete-time queue General input queue N-policy Busy period |
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