负顾客休假排队及其在信号传输中的应用

发布时间：2018-04-18 01:03

本文选题：排队系统 + 负顾客　；参考：《燕山大学》2015年硕士论文

【摘要】：随着信息技术的迅猛发展,各种各样复杂的排队系统也随之不断的涌现,尤其是带有负顾客和优先权的排队模型更具有实际的应用价值。本文研究了等待空间有限的带有负顾客、止步的、强占优先权和成批到达的三个工作休假排队模型,这些模型是已有文献中相关模型的推广。论文主要有以下三部分组成。首先考虑的是一个带有负顾客和止步的有限容量M/M/1/N单重工作休假排队系统。首先利用马尔科夫过程理论建立了系统的稳态概率所满足的方程组,并利用分块矩阵的方法求出了系统稳态概率的矩阵解;其次在此基础上得到了系统的平均等待队长、平均队长以及正顾客的损失率等性能指标;最后通过数值例子,分析了N=3时系统的参数vm和q对系统平均等待队长、顾客的消失概率这两个性能指标的影响。其次考虑的是一个带有负顾客和止步的成批到达的有限容MX/M/1/N单重工作休假排队系统。首先我们利用马尔科夫过程理论建立了系统的稳态概率所满足的方程组,并利用分块矩阵的方法求出了系统稳态概率的矩阵解;其次在此基础上得到了系统的平均等待队长、平均队长以及正顾客的损失率等性能指标;最后通过数值例子,分析了N=3时系统的参数vm和q,对系统的两个重要性能指标平均队长和顾客的消失概率的影响。最后在带有负顾客和强占优先权排队系统的基础上引入多重休假策略,考虑一个带有负顾客和强占优先权的有限容M/M/1/N多重休假排队系统。首先我们利用马尔科夫过程理论建立了系统稳态概率所满足的方程组,推导出系统稳态概率向量的迭代计算公式;其次在此基础上得到了系统的平均队长、平均等待队长以及顾客的平均损失率等性能指标;最后以N=3为例,对系统参数进行了敏感性分析。
[Abstract]:With the rapid development of information technology, a variety of complex queuing systems are emerging, especially the queuing model with negative customers and priority has more practical application value.In this paper, we study three working vacation queuing models with limited waiting space with negative customers, stop, preemptive priority and batch arrival. These models are generalizations of the related models in previous literatures.The paper is composed of three parts as follows.The first consideration is a finite capacity M/M/1/N single working vacation queuing system with negative customers and stop.In this paper, the equations of steady-state probability of the system are established by using Markov process theory, and the matrix solution of the steady-state probability of the system is obtained by using the method of block matrix, and then the average queue length of the system is obtained.Finally, the effects of the system parameters vm and Q on the average queue length and the customer vanishing probability are analyzed by numerical examples.Secondly, a finite capacity MX/M/1/N single working vacation queuing system with negative customers and stops is considered.First of all, we use Markov process theory to set up the equations satisfied by the steady-state probability of the system, and obtain the matrix solution of the steady-state probability of the system by using the method of block matrix, and then we obtain the average queue length of the system.Finally, through numerical examples, the effects of the parameters vm and qof the system with N = 3 on the average length and the customer disappearance probability of the two important performance indexes of the system are analyzed, such as the average queue length and the loss rate of the positive customer.Finally, a multiple vacation policy is introduced based on the queuing system with negative customers and preemptive priority, and a finite capacity M/M/1/N multiple vacation queueing system with negative customers and preemptive priority is considered.First of all, we establish the equations of steady-state probability of the system by using Markov process theory, and derive the iterative formula of the steady-state probability vector of the system, and then we obtain the average length of the system on the basis of which the average length of the system is obtained.The average waiting length and the average loss rate of the customer are analyzed. Finally, the sensitivity of the system parameters is analyzed by taking NN3 as an example.
【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O226

【参考文献】