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运筹学学报 ›› 2024, Vol. 28 ›› Issue (1): 29-39.doi: 10.15960/j.cnki.issn.1007-6093.2024.01.003

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带N策略的双阶段休假M/M/1排队系统驱动的流体模型性能分析

王勋1, 徐秀丽1,*()   

  1. 1. 燕山大学理学院, 河北秦皇岛 066004
  • 收稿日期:2021-11-17 出版日期:2024-03-15 发布日期:2024-03-15
  • 通讯作者: 徐秀丽 E-mail:xuxl@ysu.edu.cn
  • 基金资助:
    国家自然科学基金(62171143);河北省自然科学基金(A2019203313);河北省高等学校科学研究重点项目(ZD2019079)

Performance analysis of a fluid model driven by M/M/1 queue with $N$-policy and two-stage vacation

Xun WANG1, Xiuli XU1,*()   

  1. 1. School of Science, Yanshan University, Qinhuangdao 066004, Hebei, China
  • Received:2021-11-17 Online:2024-03-15 Published:2024-03-15
  • Contact: Xiuli XU E-mail:xuxl@ysu.edu.cn

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摘要：

基于工厂订单装配系统的运行机制, 本文构建并分析了具有N策略和两种混合休假策略的M/M/1排队系统驱动的流体模型。首先对驱动系统进行描述, 将马尔可夫过程的无穷小生成元写成块状雅克比矩阵形式。引入库存量建立三维马尔可夫过程, 得到稳态下流体排队满足的微分方程组, 运用矩阵分析方法和Laplace变换(LT) 方法得出系统平稳库存量的数学表达式。进而运用Laplace-Stieltjes变换(LST) 导出稳态条件下缓冲器的平均库存量。最后, 利用数值分析, 给出参数变化对系统性能指标的影响。

关键词: 流体模型, N策略, 双阶段休假, 库存量

Abstract:

Based on the operation mechanism of the factory order assembly system, this paper constructed and analyzed a fluid model driven by the M/M/1 queue with two type of mixed vacations and $N$ policy. Firstly, the driving system is described and the infinite small generators of the Markov process are decomposed into a blocky Jacobian matrix form. Then the three-dimensional Markov process of the fluid queue is established, the differential equations satisfied by the stationary joint distribution are obtained, and the mathematical expression of the stationary buffer content is deduced using matrix geometric solution and Laplace transformation. Then the expected buffer content is derived by Laplace-Stieltjes transformation. Finally, the influence of parameters changing on the performance indicators is illustrated by numerical analysis.

Key words: fluid model, N policy, two-stage vacation, buffer content

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