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 non-linear matrix integral equation of Volterra type. By use of the fixed point theorem of Chapter 1 the author shows that the non-linear 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