The randomized threshold for the discrete-time Geo/G/1 queue |
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Authors: | Tsung-Yin Wang Jau-Chuan Ke |
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Institution: | 1. Department of Accounting, National Taichung Institute of Technology, No. 129, Sec. 3, Sanmin Rd., Taichung 404, Taiwan, ROC;2. Department of Applied Statistics, National Taichung Institute of Technology, Taichung 404, Taiwan, ROC |
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Abstract: | This paper discusses a discrete-time Geo/G/1 queue, in which the server operates a random threshold policy, namely 〈p, N〉 policy, at the end of each service period. After all the messages are served in the queue exhaustively, the server is immediately deactivated until N messages are accumulated in the queue. If the number of messages in the queue is accumulated to N, the server is activated for services with probability p and deactivated with probability (1 − p). Using the generating functions technique, the system state evolution is analyzed. The generating functions of the system size distributions in various states are obtained. Some system characteristics of interest are derived. The long-run average cost function per unit time is analytically developed to determine the joint optimal values of p and N at a minimum cost. |
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Keywords: | Cost Busy period Discrete-time queue Markov chain Random threshold policy |
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