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Operations Research Transactions >

2025 , Vol. 29 >Issue 2: 113 - 127

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.02.009

Research Article

Analysis of M/G/1 queue with maintenance strategy and different arrival rates under service startup N-policy control

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  • School of Mathematical Sciences, Sichuan Normal University, Chengdu 610068, Sichuan, China

Received date: 2022-04-14

  Online published: 2025-06-12

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, 2025, All rights reserved. Unauthorized reproduction is prohibited.
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Abstract

Based on the background of the manufacturing system, this paper proposes an M/G/1 queuing model with maintenance strategy and different arrival rates, in which the server begins its service under the control of $N$-policy. Firstly, using the renewal process theory, total probability decomposition technique and Laplace transform, we study the transient properties of the queue length at any time $t$, and obtain the expressions of the Laplace transform of the transient queue size distribution with respect to time $t$. Then, on the basis of the transient analysis, the recursive formulas of the steady-state queue-length distribution are presented by employing L'Hospital's rule. Finally, applying the renewal reward theory, the explicit expression of the long-run expected cost per unit time of the system is obtained under a given cost structure, and numerical examples are provided to discuss the optimal control policy that the server begins its service and optimal maintenance strategy.

Key words： M/G/1 queue; maintenance strategy; service startup N-policy; queue length distribution; optimal policy

Cite this article

Fengrui LI, Yinghui TANG . Analysis of M/G/1 queue with maintenance strategy and different arrival rates under service startup N-policy control[J]. Operations Research Transactions, 2025 , 29(2) : 113 -127 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.02.009

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