A recursive method for the F-policy G/M/1/K queueing system with an exponential startup time |
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Authors: | Kuo-Hsiung Wang Ching-Chang Kuo WL Pearn |
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Institution: | 1. Department of Applied Mathematics, National Chung-Hsing University, Taichung 402, Taiwan;2. Department of Industrial Engineering and Management, National Chiao Tung University, Hsin Chu 30050, Taiwan |
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Abstract: | This paper deals with the optimal control of a finite capacity G/M/1 queueing system combined the F-policy and an exponential startup time before start allowing customers in the system. The F-policy queueing problem investigates the most common issue of controlling arrival to a queueing system. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining interarrival time, to develop the steady-state probability distribution of the number of customers in the system. We illustrate a recursive method by presenting three simple examples for exponential, 3-stage Erlang, and deterministic interarrival time distributions, respectively. A cost model is developed to determine the optimal management F-policy at minimum cost. We use an efficient Maple computer program to determine the optimal operating F-policy and some system performance measures. Sensitivity analysis is also studied. |
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Keywords: | F-Policy G/M/1/K queue Recursive method Server startup Supplementary variable |
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