The Solution of Quasi Birth and Death Processes Arising from Multiple Access Computer Systems.
Abstract
Quasi birth and death processes (QBD-processes) are continuous time Markov chains whose transition intensity matrices can be represented in tri-diagonal block form, with the blocks along a diagonal being identical submatrices after the first. They are a general class of infinite state Markov chains which are useful as models of the 'high traffic' behavior of large, multiple-access computer systems. Classical queuing theory offers no general technique for determination of equilibrium distributions of QBD-processes, particularly not for QBD-processes of the degree of complexity likely to be encountered in computer applications. However, the equilibrium equations can be shown to have a formal similarity to the equilibrium equations of simple birth and death processes with matrices and vectors in the former replacing scalars in the latter. R. V. Evans has proposed that this similarity be used to derive a numerical procedure which involves several separate finite operations, each of which does not tax the memory or computing capabilities of a moderately large digital computer. The dissertation rigorously develops the procedure, primarily through the use of modern analysis, matrix theory, and generalized difference equations.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1969
- Accession Number
- AD0853351
Entities
People
- Victor L. Wallace
Organizations
- University of Michigan