| 引用本文: | 杨镇铭,赵千川.闭环Jackson网络的资源利用率分析方法及应用[J].控制理论与应用,2021,38(11):1819~1827.[点击复制] |
| YANG Zhen-ming,ZHAO Qian-chuan.Analysis and application of resource utilization in closed Jackson networks[J].Control Theory and Technology,2021,38(11):1819~1827.[点击复制] |
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| 闭环Jackson网络的资源利用率分析方法及应用 |
| Analysis and application of resource utilization in closed Jackson networks |
| 摘要点击 1757 全文点击 417 投稿时间：2021-08-23 修订日期：2021-11-24 |
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| DOI编号 10.7641/CTA.2021.10774 |
| 2021,38(11):1819-1827 |
| 中文关键词 排队网络 闭环Jackson网络 资源利用率 自动化码头 |
| 英文关键词 queueing networks closed Jackson network resource utilization automated container terminals |
| 基金项目 国家自然科学基金项目(61425027), 111引智计划项目(BP2018006), 北京信息科学与技术国家研究中心项目(BNR2019TD01009)资助. |
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| 中文摘要 |
| 排队网络是一种常见的对供应链、生产线以及交通系统等进行建模的工具, 可以被用来分析系统中各资源
的利用率, 并对系统结构的设计提供指导. 相比较于利用仿真进行分析, 排队网络可以更快速地得到系统的资源利
用率. 在实际中, 常用闭环Jackson网络来对顾客总数不变的封闭系统进行建模. 在本文中, 首先利用闭环Jackson网
络归一化参数的母函数, 得到了网络中各节点利用率的解析表达式. 通过对利用率解析表达式的分析, 给出了在顾
客总数趋于无穷时利用率的极限, 并证明了利用率是饱和函数. 在这些结论的基础上, 进一步计算不同服务时间下
达到饱和状态所需的顾客总数. 最后将该方法应用于一个实际的自动化码头例子, 将其建模为闭环Jackson网络, 分
析码头的瓶颈所在, 计算系统饱和点对应的车辆数, 并与仿真实验进行了对比. |
| 英文摘要 |
| Queueing networks are widely used in modeling supply chains, assembly lines and transportation systems.
The analytical results of queueing networks can help comparing the efficiency of different configurations and providing
guidance for system design. Closed Jackson network (CJN) is frequently used to model these systems. In this paper, based
on the generating function of the closed Jackson network’s normalized parameters, the utilization’s analytical expression
is obtained. It is also proved that the limit of utilization exists when the total number of customers tends to infinity, and
utilization is a saturation function. Then the saturation point, which is the total number of customers required to reach
saturation state, can be calculated. Finally, this method is applied to a queuing network modeled from an actual automated
terminal to analyze the bottleneck and the saturation vehicle number of the terminal. The results from the closed Jackson
network are close to the results from simulation experiments. So queueing network is a feasible method to analyze the
performance of systems like container terminals. |
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