带有灾难和伯努利休假的排队系统的研究

发布时间：2018-01-13 16:02

本文关键词：带有灾难和伯努利休假的排队系统的研究　出处：《南京理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着计算机网络和通信系统的快速发展,带有灾难的排队系统越来越受重视。近20年,伴有灾难发生的排队系统被学者们广泛研究。常见的这类排队系统主要有两种消除机制:一种是部分消除,另一种是全部消除。本文研究了三类基于全部消除的带有伯努利休假的排队系统。模型一是带有灾难、维修和伯努利休假的M/M/1排队系统,并且已发表在 Journal of Systems Science and Information 上。首先,获得了系统中顾客数的概率母函数(PGF)和一些性能指标。其次,推导了顾客逗留时间分布的Laplace-Stieltjes变换(LST)和平均逗留时间。最后,通过数值例子展现不同参数对平均顾客数的影响。在模型一的基础上,模型二考虑了启动期和关闭期。二者常用在机器生产系统中,起到降低成本节省能量的作用。首先,通过解平衡方程,获得了系统中顾客数的PGF和服务员处于不同状态的概率。其次,通过强马尔可夫性,推导了顾客逗留时间分布的LST和平均逗留时间。最后,通过数值例子分析参数对平均队长和系统处于空闲状态的概率的影响。在模型一的基础上,模型三考虑了启动期,并将服务时间的分布推广到一般分布。利用补充变量技术和儒歇定理,获得了系统中顾客数的PGF和一些性能指标。接着,对带有启动期、灾难和维修的M/G/1排队系统进行循环分析(一个循环是指两次连续的维修结束时刻之间的长度),得到循环长度的LST和平均循环长度。
[Abstract]:With the rapid development of computer network and communication system, queueing system with disaster has been paid more and more attention for nearly 20 years. Queuing systems with disasters have been widely studied by scholars. There are two kinds of mechanisms to eliminate these queuing systems: one is partial cancellation. In this paper, we study three classes of queueing systems with Bernoulli vacation based on total elimination. The first model is the M / M / 1 queue system with disaster, maintenance and Bernoulli vacation. And has been published in the Journal of Systems Science and Information. The probabilistic generating function (PGFs) and some performance indexes of customer number in the system are obtained. The Laplace-Stieltjes transform of customer sojourn time distribution and the average sojourn time are derived. Finally. Numerical examples show the influence of different parameters on the average number of customers. On the basis of model 1, model 2 takes into account the start-up period and the closing period. Both of them are commonly used in the machine production system. First, by solving the equilibrium equation, we get the probability that the customer number of PGF and the waiter are in different states. Secondly, through the strong Markov property. The LST and average sojourn time of customer sojourn distribution are derived. Finally, the influence of parameters on the average length of queue and the probability of the system in idle state is analyzed by numerical examples. Model 3 takes into account the start-up period and extends the distribution of service time to general distribution. By using the complementary variable technique and the Rouche theorem, the PGF and some performance indexes of the customer number in the system are obtained. The M / G / 1 queueing system with start-up, disaster, and maintenance is cyclically analyzed (a cycle is the length between the end of two successive repairs). The LST of cycle length and the average cycle length are obtained.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O226

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