
Accession Number : AD0737251
Title : On the Use of Analytic Matric Functions in Queueing Theory,
Corporate Author : PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS
Personal Author(s) : Purdue,Peter
Report Date : JAN 1972
Pagination or Media Count : 73
Abstract : In the thesis the author defines an analytic matric function F(.) by F(X) = the summation from N = 0 to infinity of ((F sub N)(X sup N)) where F sub n, X are mxm complex matrices. In chapter 1 the author discusses a fixed point theorem for such functions and then in subsequent chapters he analyzes various queueing models where these occur. The basic problem in each of the queueing models analyzed reduces to the solution of a nonlinear matrix integral equation of Volterra type. By use of the fixed point theorem of Chapter 1 the author shows that the nonlinear integral equation has a unique solution. The complete transient behavior of each queue may be expressed in terms of the solution of the integral equation. For each model, the equilibrium condition is also determined. (Author)
Descriptors : (*QUEUEING THEORY, ANALYTIC FUNCTIONS), MATRICES(MATHEMATICS), STOCHASTIC PROCESSES, INTEGRAL EQUATIONS, BANACH SPACE, CONVEX SETS, MAPPING(TRANSFORMATIONS), STATISTICAL PROCESSES, THEOREMS
Subject Categories : Statistics and Probability
Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE