学校logo 学校名毕业设计(论 文)
排队论在校园网中的应用
系 别 专 业 班级学号 姓 名 指导教师
20**年06月15日
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****毕业设计（论文）
第 I 页
排队论在校园网中的应用
摘 要
本论文首先介绍了排队论的基本知识，主要研究排队模型中的被服务者到达间隔的分布和服务时间的分布，对系统运行指标和系统状态平衡方程进行了详细的计算和推导，着重介绍了单服务台和多服务台的标准模型，其中多服务台系统容量有限制的模型是本论文解决问题的基础模型．排队模型中被服务者到达间隔的分布和服务时间的分布的确定分别用到了概率论中的泊松分布和负指数分布．
本论文的模型应用部分，通过对校园网随机服务系统中，服务质量与系统资源间矛盾的分析，应用排队论的原理，建立数学模型，将M/M/c/N/?模型应用到校园网的设计和调节收费问题中，并分别用LINGO和MATLAB数学软件辅助求解，制定出一套校园网收费系统，以达到提高校园网使用效率、提高服务质量的目的．最后对研究结果进行了总结，指出了优点和不足．
关键词：排队论，泊松分布，运行指标，M/M/n/n/?模型
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****毕业设计（论文）
第 II 页
The application of Queuing theory in Campus Network
Author:
Tutor:
Abstract
The paper first introduces the basic knowledge of queuing theory, especially the service interval distribution and arrival time distribution, then calculates and derives the system indicators and the balance equation of the system state in detail, and focus on the standard single-desk queuing model and standard multi-server queuing model. The model which capacity is limited is the basis model to solve the problem in this paper.The Poisson distribution of Probability Theory and negative exponential distribution were used to determine the service interval distribution and arrival time distribution in the queuing model .
By analysing the contradictions between quality of service and system resources in the Campus Network stochastic service system and the application of the queuing theory, the model is established. The mathematics software LINGO and MATLAB are used to solute the
M/M/c/N/? model. The charging system of Campus Network is lay down to improve
efficiency in the use of campus network and the quality of services. Finally, the paper summarizes the results, pointing out the advantages and disadvantages of the paper.
Key Words: Queuing theory, Poisson distribution, Operation indicators，M/M/n/n/?
model
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****毕业设计（论文）
第 III 页
目 录
1 绪论 ...................................................................................................................................... 1
1.1 论文的选题背景及意义 ............................................................................................. 1 1.2 本文的主要工作 ......................................................................................................... 2 2 排队论基础 .......................................................................................................................... 3
2.1 排队论的基本概念 ..................................................................................................... 3
2.1.1 排队过程的一般模型 ...................................................................................... 3 2.1.2 排队系统的运行指标 ...................................................................................... 4 2.1.3 系统状态的概率 .............................................................................................. 5 2.1.4 到达时间的间隔分布和服务时间的分布 ...................................................... 5 2.2 排队模型及其分类 ..................................................................................................... 7
2.2.1 排队模型的一般表示 ...................................................................................... 7 2.2.2 排队模型的分类 .............................................................................................. 8 2.3 单服务台的标准模型 ................................................................................................. 8 2.4 多服务台的标准模型 ............................................................................................... 11 3 校园网的设计和调节收费问题 ........................................................................................ 13
3.1 问题的提出 ............................................................................................................... 13 3.2 问题的分析与假设 ................................................................................................... 13 3.3 模型的建立 ............................................................................................................... 14
3.3.1 LINGO相关知识介绍 ..................................................................................... 14 3.3.2 MATLAB曲线拟合 ......................................................................................... 15 3.3.3 系统容量有限制的排队模型M/M/c/N/? ............................................. 16 3.4 模型的应用与求解 ................................................................................................... 18 结 论 .................................................................................................................................. 23 致 谢 .................................................................................................................................. 24 参考文献 .................................................................................................................................. 25 附 录 ................................................................................................................................ 26
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