A recursive method to the optimal control of an M/G/1 queueing system with finite capacity and infinite capacity |
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Authors: | Kuo-Hsiung Wang Jau-Chuan Ke |
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Affiliation: | Department of Applied Mathematics, National Chung-Hsing University, Taichung 402, Taiwan, ROC |
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Abstract: | We study a single removable server in an infinite and a finite queueing systems with Poisson arrivals and general distribution service times. The server may be turned on at arrival epochs or off at service completion epochs. We present a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining service time, to obtain the steady state probability distribution of the number of customers in a finite system. The method is illustrated analytically for three different service time distributions: exponential, 3-stage Erlang, and deterministic. Cost models for infinite and finite queueing systems are respectively developed to determine the optimal operating policy at minimum cost. |
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Keywords: | Cost Control M/G/1 queue Recursive method Supplementary variable |
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