交互环境下几类排队系统分析

发布时间：2018-07-11 09:40

本文选题：交互随机环境 + 灾难　；参考：《南京理工大学》2017年硕士论文

【摘要】：在最近的几十年里,由于排队论在现代复杂通信网络中的重要应用,在随机环境下研究排队模型已成为一种热潮,并且极具现实意义。在拥有多个随机环境的排队系统中,环境之间会按照一定的规则进行跳转,每个环境都有其相应的顾客的到达率以及服务员的服务率。本文在交互环境(2阶随机环境)下研究排队系统,主要分析三个排队模型。模型一为交互环境下带有专有维修环境的M/G/1可修排队系统。在服务员服务期间,系统可能会发生灾难,导致服务中断,并且系统中所有顾客必须离开系统,服务台在专有的维修环境下进行维修。在该模型的分析中,我们求出了系统的稳态分布以及平均队长、服务员空闲的概率等性能指标。模型二为交互环境下带有批服务的轮循排队系统,也是对Israeli队列的研究。运用矩阵分析和谱分析两种方法求出了系统队长的稳态分布,并给出了在主队列已满的条件下,选择进入等待区域的顾客的条件等待时间以及等待区域的平均队长等性能指标。模型三为交互环境下带有启动时间的清空排队系统。该模型是基于现实生活中的交通服务系统。从经济学角度,基于"收入—支出"结构,分别从可见和不可见两种情形分析了顾客的止步策略。对于上述讨论的模型,我们分别进行了数值分析,用以说明特定参数对各性能指标的影响。
[Abstract]:In recent decades, because of the important application of queuing theory in modern complex communication networks, the study of queuing model in random environment has become a kind of upsurge and has great practical significance. In queueing systems with multiple random environments, each environment has its corresponding arrival rate of customers and service rate of waiters according to certain rules. In this paper, the queuing system is studied in the interactive environment (2 order random environment), and three queuing models are analyzed. Model one is an M / G / 1 repairable queuing system with proprietary maintenance environment in interactive environment. During the server service, the system may suffer a disaster, resulting in service disruption, and all customers in the system must leave the system, the help desk in a proprietary maintenance environment to carry out maintenance. In the analysis of the model, we obtain the steady-state distribution of the system, the average queue length, the idle probability of waiters and other performance indicators. The second model is an iterative queuing system with batch service in interactive environment, and it is also a study of Israeli queue. The steady-state distribution of system queue length is obtained by using matrix analysis and spectral analysis, and the performance indexes such as the conditional waiting time of the customer entering the waiting area and the average queue length of the waiting area are given under the condition that the main team column is full. Model 3 is an empty queuing system with startup time in interactive environment. The model is based on the real-life traffic service system. From the point of view of economics, based on the structure of "income-expenditure", this paper analyzes the stopping strategies of customers from the two situations of visible and invisible. The models discussed above are numerically analyzed to illustrate the effects of specific parameters on each performance index.
【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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