Eigen-Interval And Eigen-Interval Vectors Of Interval Matrics In Interval Max-Plus Systems

The production period has important application in the performance evaluation of computer networks,automated manufacturing plants.For a manufacturing system with input structure,we need not to consider the input time of raw materials,only consider the transportation time and processing time.So,this is autonomous system that is familiar to us.While the delivery time and processing time of the parts in the production system are often in the form of intervals,by researching the solutions and algorithms of the state equations of interval max-plus systems,we can compute the eigen-interval and corresponding eigen-interval vectors of irreducible interval matric of interval max-plus systems and then get the production period.Subiono gave the mathematical expression of the eigenvalue and eigenvector of the irreducible matrix in max-plus system and the calculation method of the production cycle.In this paper,we mainly give the mathematical expression and the calculation method of the eigen-interval and eigen-interval vector of irreducible interval matrix in the interval max-plus system.Firstly,we give the equation of state equation and the solution of the interval max-plus system.We introduction the eigen-interval vector,the irreducible interval matrix,the interval average weight,the periodic time interval vector,the interval event graph,etc.When the interval max-plus system has only one eigeninterval,for the initial state including at least one finite interval component in the interval vector,after a series of iterations,the interval max-plus system presents the periodicity,and the interval average weight is equal to the eigen-interval and unique,and then the specific mathematical expression of the eigen-interval and the eigen-interval vector is given and eigen-interval and eigen-interval vector calculation method,so as to extend the algorithm of the original max-plus system to the interval max-plus system.