On the Use of Analytic Matric Functions in Queueing Theory,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1972
- Accession Number
- AD0737251
Entities
People
- Peter Purdue
Organizations
- Purdue University