Optimal Control Policy of M/G/1 Queueing System with Delayed Randomized Multiple Vacations Under the Modified Min(N, D)-Policy Control

doi:10.1007/s40305-022-00413-9

Journal of the Operations Research Society of China ›› 2023, Vol. 11 ›› Issue (4): 857-874.doi: 10.1007/s40305-022-00413-9

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Optimal Control Policy of M/G/1 Queueing System with Delayed Randomized Multiple Vacations Under the Modified Min(N, D)-Policy Control

Le Luo^1,2, Ying-Hui Tang¹, Miao-Miao Yu¹, Wen-Qing Wu³

1. School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610068, Sichuan, China;
2. Nanchong Vocational and Technical College, Nanchong, 637000, Jiangsu, China;
3. Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu, 610068, Sichuan, China

Received:2021-06-29 Revised:2022-02-27 Online:2023-12-30 Published:2023-12-26
Contact: Ying-Hui Tang, Le Luo, Miao-Miao Yu, Wen-Qing Wu E-mail:tangyh@sicnu.edu.cn;18990722176@163.com;mmyu75@163.com;wwqing0704@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (No. 71571127) and the National Natural Science Youth Foundation of China (No. 72001181).

Abstract

Abstract: Based on the number of customers and the server’s workload, this paper proposes a modified Min(N, D)-policy and discusses an M/G/1 queueing model with delayed randomized multiple vacations under such a policy. Applying the well-known stochastic decomposition property of the steady-state queue size, the probability generating function of the steady-state queue length distribution is obtained. Moreover, the explicit expressions of the expected queue length and the additional queue length distribution are derived by some algebraic manipulations. Finally, employing the renewal reward theorem, the explicit expression of the long-run expected cost per unit time is given. Furthermore, we analyze the optimal policy for economizing the expected cost and compare the optimal Min(N, D)-policy with the optimal N-policy and the optimal D-policy by using numerical examples.

Key words: M/G/1 queue, Modified Min(N, D)-policy, Randomized multiple vacations, Queue length generating function, Optimal joint control policy

CLC Number:

60K25
90B22

Le Luo, Ying-Hui Tang, Miao-Miao Yu, Wen-Qing Wu. Optimal Control Policy of M/G/1 Queueing System with Delayed Randomized Multiple Vacations Under the Modified Min(N, D)-Policy Control[J]. Journal of the Operations Research Society of China, 2023, 11(4): 857-874.

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Optimal Control Policy of M/G/1 Queueing System with Delayed Randomized Multiple Vacations Under the Modified Min(N, D)-Policy Control

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