基于启动时间和完全故障的双阶段休假排队系统的流体模型性能分析

数学物理学报 ›› 2024, Vol. 44 ›› Issue (4): 1092-1109.

基于启动时间和完全故障的双阶段休假排队系统的流体模型性能分析

徐秀丽¹(),张怡通^2,^*(),王勋¹(),刘洺辛³()

¹燕山大学理学院河北秦皇岛 066004
²燕山大学经济管理学院河北秦皇岛 066004
³广东海洋大学电子与信息工程学院广东湛江 524088

收稿日期:2023-07-31 修回日期:2024-01-25 出版日期:2024-08-26 发布日期:2024-07-26
通讯作者: *张怡通, E-mail: YitongZz@126.com
作者简介:徐秀丽, E-mail: xxl-ysu@163.com;王勋, E-mail: 2635388468@qq.com;刘洺辛, E-mail: mingxinliu001@sina.com.cn
基金资助:
国家自然科学基金(62171143)

Performance Analysis of Fluid Model Based on Two-Stage Vacation Queue with Set-Up Time and Complete Failure

Xu Xiuli¹(),Zhang Yitong^2,^*(),Wang Xun¹(),Liu Mingxin³()

¹School of Sciences, Yanshan University, Hebei Qinhuangdao 066004
²School of Economics and Management, Yanshan University, Hebei Qinhuangdao 066004
³School of Electronics and Information Engineering, Guangdong Ocean University, Guangdong Zhanjiang 524088

Received:2023-07-31 Revised:2024-01-25 Online:2024-08-26 Published:2024-07-26
Supported by:
NSFC(62171143)

摘要/Abstract

摘要：

基于风力发电路灯的能量转化机制, 该文构建并分析了具有启动时间和完全故障策略的 M/M/1 排队系统驱动的流体模型. 首先, 对驱动系统进行模型描述, 运用矩阵几何解方法得到驱动系统的稳态概率分布. 其次, 引入流体模型的净输入率结构, 并利用概率分析方法得到流体库存水平在稳态条件下的微分差分方程组, 进而运用 Laplace-Stieltjes transform(LST) 方法得到稳态条件下库存量的均值及空库概率. 根据性能指标构建系统的费用函数, 在数值分析中给出系统参数对性能指标和费用的影响.

关键词: 流体模型, 双阶段休假, 启动时间, 完全故障, 库存量

Abstract:

Based on the energy conversion mechanism of wind power street lamps, this paper constructed and analyzed a fluid model driven by the M/M/1 queueing system with set-up time and complete failure. Firstly, the driving system is described and the stationary probability distribution of the driving system is obtained by using the matrix-geometry method. Secondly, the differential and difference equations of the fluid level in steady-state conditions are obtained based on the net input rate structure of the fluid model and using the probability analysis method. Then, the expected buffer content and the probability of the empty buffer under steady-state conditions are obtained by using the Laplace-Stieltjes transform(LST) method. The cost function of the system is constructed according to the performance index. Finally, the influence of parameters changing on the performance indicators and cost function are illustrated in numerical analysis.

Key words: Fluid model, Two-stage vacation, Set-up time, Complete failure, Buffer content

中图分类号:

O226

徐秀丽, 张怡通, 王勋, 刘洺辛. 基于启动时间和完全故障的双阶段休假排队系统的流体模型性能分析[J]. 数学物理学报, 2024, 44(4): 1092-1109.

Xu Xiuli, Zhang Yitong, Wang Xun, Liu Mingxin. Performance Analysis of Fluid Model Based on Two-Stage Vacation Queue with Set-Up Time and Complete Failure[J]. Acta mathematica scientia,Series A, 2024, 44(4): 1092-1109.

图/表 6

图1

图2

图3

图4

图5

图6

参考文献 17

[1]	Virtamo J, Norros I. Fluid queue driven by an M/M/1 queue. Queueing Systems, 1994, 16(3/4): 373-386
[2]	Adan I, Resing J. Simple analysis of a fluid queue driven by an M/M/1 queue. Queueing Systems, 1996, 22(1/2): 171-174
[3]	Kulkarni V G. Fluid models for single buffer systems. Econometrica, 1997, 40(5): 321-338
[4]	Sericola B, Tuffin B. A fluid queue driven by a Markovian queue. Queueing Systems Theory and Applications, 1999, 31(3/4): 253-264
[5]	Lierde S V, Soares A S, Latouche G. Invariant measures for fluid queues. Stochasyic Models, 2008, 24(1): 133-151
[6]	Ammar, Sherif I. Fluid queue driven by an M/M/1 disasters queue. International Journal of Computer Mathematics, 2014, 91(7): 1497-1506
[7]	Wang F W, Mao B W. Fluid model driven by an M/M/1 queue with set-up and close-down period. Applied Mechanics and Materials, 2014, 513-517: 3377-3380
[8]	徐秀丽, 王现英, 李晓庆. 具有可选服务的 M/M/1 排队驱动的流模型. 西北师范大学学报(自然科学版), 2016, 52(1): 21-24
	Xu X L, Wang X Y, Li X Q. Fluid model driven by an M/M/1 queue with optional service. Journal of Northwest Normal University (Natural Science), 2016, 52(1): 21-24
[9]	孙红霜. 带有工作故障的 M/M/1 重试排队流模型的系统性能分析. 南京: 南京信息工程大学, 2022
	Sun H S. Performance analysis of the fluid model driven by M/M/1 queue with working breakdown strategies and retrial strategy. Nanjing: Nanjing University of Information Science and Technology, 2022
[10]	Ammar, Sherif I. Analysis of an M/M/1 driven fluid queue with multiple exponential vacations. Applied Mathematics and Computation, 2014, 227: 329-334
[11]	Mao B W, Wang F W, Tian N S. Fluid model driven by an M/M/1/N queue with exponential vacations. Journal of Computational Information Systems, 2010, 6(6): 1809-1816
[12]	Vijayashree K V, Anjuka A. Fluid queue modulated by an M/M/1/N queue subject to multiple exponential working vacation. International Journal of Pure and Applied Mathematics, 2017, 113(13): 153-162
[13]	徐秀丽, 王现英, 徐彪. 可选服务的 M/M/1 多重休假排队系统驱动的流模型. 数学的实践与认识, 2018, 48(6): 155-161
	Xu X L, Wang X Y, Xu B. A fluid model driven by an M/M/1 vacations queue with optional service. Mathematics in Practice and Theory, 2018, 48(6): 155-161
[14]	Xu X L, Wang X Y, Song X F, et al. Fluid model modulated by an M/M/ 1 working vacation queue with negative customer. Acta Mathematicae Applicatae Sinica-English Series, 2018, 34(2): 404-415
[15]	刘煜飞, 叶晴晴. 基于矩阵分析方法的具有双阶段休假的排队系统驱动的流模型性能分析. 数学的实践与认识, 2021, 51(4): 189-199
	Liu Y F, Ye Q Q. Performance analysis of the fluid model driven by M/M/1 queuing system with two-stage vacation based on matrix analysis method. Mathematics in Practice and Theory, 2021, 51(4): 189-199
[16]	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. 数学物理学报, 2021, 41A(1): 254-268
	Li Z K, Xu X L, Yue D Q. Analysis of the fluid model driven by M/M/c queue with single working vacation. Acta Mathematica Sci, 2021, 41A(4): 254-268
[17]	王勋, 徐秀丽. 基于启动时间和可选服务的双阶段休假排队系统的流体模型性能分析. 数学物理学报, 2023, 43A(6): 1943-1960
	Wang X, Xu X L. Performance analysis of a fluid model driven by two-stage vacation queue with set-up time and optimal service. Acta Mathematica Sci, 2023, 43A(6): 1943-1960