区间极大加系统中区间矩阵的特征区间与特征区间向量

发布时间：2018-03-20 21:29

本文选题：双子　切入点：区间极大加系统　出处：《河北师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：生产周期在计算机网络、自动化制造和数字电路等系统的性能评估中有着重要的应用.对于带有输入结构的生产系统,在不考虑原料的输入时间,只考虑零件的传递时间和机器的加工时间时便成为了我们熟悉的自治的生产系统.而生产系统中零件的传递时间和加工时间往往以区间的形式出现,通过研究区间极大加系统的状态方程的解和算法,就可以计算出区间极大加系统中不可约区间矩阵的特征区间和特征区间向量,从而得到整个系统的生产周期,即特征区间.Subiono给出了极大加系统中不可约矩阵的特征值与特征向量的数学表达式及生产周期的计算方法.本文主要研究了区间极大加系统中不可约区间矩阵的特征区间与特征区间向量的数学表达式及生产周期的计算方法.首先给出了区间极大加系统的状态方程及解的表达式.定义了特征区间及特征区间向量、不可约区间矩阵、区间平均权重、周期时间区间向量、区间事件图等概念.在区间极大加系统有且仅有一个特征区间时,对于至少包含一个有限区间分量的初始状态区间向量而言,经过一系列迭代,区间极大加系统呈现出周期性,得到了区间平均权重等于特征区间且唯一,进而给出了特征区间与特征区间向量的具体数学表达式和特征区间及特征区间向量的计算方法,从而将原有的极大加系统中的算法推广到了区间极大加系统中.
[Abstract]:Production cycle plays an important role in evaluating the performance of computer networks, automated manufacturing and digital circuits. For production systems with input structures, the input time of raw materials is not considered. Considering only the transfer time of the parts and the processing time of the machine, it becomes a familiar autonomous production system, and the transfer time and the processing time of the parts in the production system often appear in the form of interval. By studying the solution and algorithm of the state equation of the interval maximum additive system, the characteristic interval and the characteristic interval vector of the irreducible interval matrix in the interval maximum addition system can be calculated, and the production cycle of the whole system can be obtained. Namely, characteristic interval. Subiono gives the mathematical expression of the eigenvalue and eigenvector of the irreducible matrix in the maximal additive system and the method of calculating the production cycle. In this paper, we mainly study the special properties of the irreducible interval matrix in the interval maximal additive system. The mathematical expressions of eigeninterval vector and eigeninterval vector and the method of calculating the production cycle are given. Firstly, the state equation and the expression of the solution of the interval maximum additive system are given, and the characteristic interval and the eigeninterval vector are defined. The concepts of irreducible interval matrix, interval average weight, periodic time interval vector, interval event graph, and so on. For the initial state interval vector containing at least one finite interval component, after a series of iterations, the interval maximum addition system presents periodicity, and the interval average weight is equal to the characteristic interval and is unique. Furthermore, the mathematical expressions of feature interval and feature interval vector and the calculation method of feature interval and feature interval vector are given, which generalizes the algorithm of the original maximal addition system to the interval maximum addition system.
【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O151.21

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