单重工作休假M/M/c排队驱动的流体模型分析

数学物理学报 ›› 2021, Vol. 41 ›› Issue (1): 254-268.

单重工作休假M/M/c排队驱动的流体模型分析

李子坤,徐秀丽*(),岳德权

燕山大学理学院河北秦皇岛 066000

收稿日期:2019-10-14 出版日期:2021-02-26 发布日期:2021-01-29
通讯作者: 徐秀丽 E-mail:xxl-ysu@163.com
基金资助:
国家自然科学基金(71971189);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)

Analysis of the Fluid Model Driven by M/M/c Queue with Single Working Vacation

Zikun Li,Xiuli Xu*(),Dequan Yue

School of Science, Yanshan University, Hebei Qinhuangdao 066000

Received:2019-10-14 Online:2021-02-26 Published:2021-01-29
Contact: Xiuli Xu E-mail:xxl-ysu@163.com
Supported by:
the NSFC(71971189);the NSF of Hebei Province(A2019203313);the Key Project of Scientific Research in Higher Education of Hebei Province(ZD2019079)

摘要/Abstract

摘要：

该文在M/M/c排队驱动系统中加入工作休假策略，研究了单重工作休假多服务台排队驱动的流体模型.利用拟生灭过程和矩阵几何解法得到驱动系统稳态队长分布.构建净输入率结构，导出流体模型的稳态联合分布函数满足的的矩阵微分方程组，进而利用Laplace-Stieltjes变换(LST)方法得到稳态下缓冲器库存量的空库概率及均值表达式.最后，给出模型在多信道无线Mesh网下的应用，通过数值例子展示参数变化对系统性能指标的影响.

关键词: 流体模型, 单重工作休假, 库存量, 无线Mesh网

Abstract:

In this paper, introducing working vacation strategy into an M/M/c queue, the fluid model driven by a multi-server queue with single working vacation is studied. Using quasi birth-and-death process and matrix-geometric method, the steady-state distribution of the queue length is obtained.The net input rate structure is constructed, and the matrix differential equations satisfied by the joint stationary distribution of the fluid model are derived. Furthermore, by using Laplace-Stieltjes Transform (LST) method, the probability of the empty buffer content and the mean of the buffer content in the stable case are obtained. Finally, the application of the model in multi-channel wireless Mesh network is presented, and the influence of parameter on system performance index is demonstrated in numerical examples.

Key words: Fluid model, Single working vacation, Buffer content, Wireless Mesh network

中图分类号:

O226

李子坤,徐秀丽,岳德权. 单重工作休假M/M/c排队驱动的流体模型分析[J]. 数学物理学报, 2021, 41(1): 254-268.

Zikun Li,Xiuli Xu,Dequan Yue. Analysis of the Fluid Model Driven by M/M/c Queue with Single Working Vacation[J]. Acta mathematica scientia,Series A, 2021, 41(1): 254-268.

图/表 2

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