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Service Rate Control in Mn/Gn/1 Queue

Abstract : Service rate control in queues is an important problem in practice. For example, when the number of customers waiting for finished products is small production has a normal speed, but if it is greater, the production speed should be faster to meet the demand. For an exponential service time distribution, the optimality of the threshold type policy has been proved in literature. On the other hand, in production systems, production time follows a general distribution in general. In this paper, service control of speed depending on the number of customers is discussed. The analytical results of an M/G/1 queue with arrival and service rates depending on the number of customers in the system, which is called an Mn/Gn/1 queue, are utilized for computing performance measure of service rate control. Constant, uniform and exponential distributions on the service time are considered through numerical experiments. The results show that the optimal threshold depends on the type of the distributions even when the mean of service time is the same.
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Koichi Nakade, Shunta Nishimura. Service Rate Control in Mn/Gn/1 Queue. IFIP International Conference on Advances in Production Management Systems (APMS), Aug 2018, Seoul, South Korea. pp.289-296, ⟨10.1007/978-3-319-99704-9_35⟩. ⟨hal-02164849⟩

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