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A SYSTEM FOR THE SOLUTION OF SIMPLE STOCHASTIC NETWORKS

IP.com Disclosure Number: IPCOM000128405D
Original Publication Date: 1969-Sep-01
Included in the Prior Art Database: 2005-Sep-15

Publishing Venue

Software Patent Institute

Related People

Irani, Keki B.: AUTHOR [+4]

Abstract

This report details the data and program structures for a conversational programming system which translates commands describing a Markovian queueing network into a matrix of transition intensities, and which provides equilibrium distributions and related solutions of the network according to requested specifications.

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This is the abbreviated version, containing approximately 3% of the total text.

Page 1 of 48

THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

A SYSTEM FOR THE SOLUTION OF SIMPLE STOCHASTIC NETWORKS

THE UNIVERSITY OF MICHIGAN Technical Report 14 Keki B. Irani Victor L. Wallace

CONCOMP: Research in Conversational Use of Computers
F. H. Westervelt, Project Director ORA Project 07449

supported by ADVANCED RESEARCH PROJECTS AGENCY DEPARTMENT OF DEFENSE WASHINGTON, D. C.

CONTRACT NO. DA-49-083 OSA-3050 ARPA ORDER NO. 716

administered through: OFFICE OF RE SEARCH ADMINISTRATION ANN ARBOR

September 1969

Abstract

This report details the data and program structures for a conversational programming system which translates commands describing a Markovian queueing network into a matrix of transition intensities, and which provides equilibrium distributions and related solutions of the network according to requested specifications.

Table of Contents

List of Figures.....vi
List of Tables.....viii
Preface.....ix
1. Introduction.....1
2. The Basic Compilation and Calculation Philsophy.....5
3. The Generation Process and Network Syntax.....11
4. Primitive Elements and Their Meaning.....29
5. The Compilation Process.....43
6. The State and Transition-Matrix Structures.....91
7. The Solution for Equilibrium Probabilities.....107
8. Specification and Calculation of Results.....113
9. Epilogue.....125

University of Michigan Page 1 Sep 01, 1969

Page 2 of 48

A SYSTEM FOR THE SOLUTION OF SIMPLE STOCHASTIC NETWORKS

References.....131
Appendix A.....133

List of Figures

2.1 Supervisor Flow Diagram.....9
3.1 A Diagram.....14
3.2 A Fragment of a Completed Network Structure.....19
3.3 Network Structure Diagram Notation.....20
3.4 Network Structure Fragment Showing Symbol Table and Unconnected Port Set R.....24
4.1 Fragment of Network Structure Showing Literal Type Definition.....36
4.2 Format of τ-line of Element.....38
4.3 The Set Structure for n-Tuples.....41
4.4 The n-Tuple Set Head Word.....41
5.1 Illustrating the Compilation Procedure.....45
5.2 The Compiler Flow Diagram.....46
5.3 Flow Diagram for "Collect Associates" Routine.....54
5.4 Fragment of Working Structure upon Entry to "Collect Associates" Routine.....55
5.5 Status of Working Structure at β in Figure 5.2.....56
5.6 Result of Collection Operation on Figure 5.3.....57
5.7 Flow Diagram of Absorption of Connections.....68
5.8 Fragment of Working Network Structure at Beginning of Connection Absorption.....70
5.9 Fragment of Working Network Structure, Prepatory to Generating Spontaneous Events.....71

List of Figures (Continued)

5.10 Prototype Flow Diagram for Spontaneous Event Routines.....73
5.11 Fragment of Working Network Structure upon Exit from Spontaneous Event Routine.....75
5.12 Flow Diagram: Event Consolidation.....78
5.13 Flow Diagram: Event Set Consolidation.....79
5.14 A Network Fragment Containing a Random Branch.....81
5.15 Communication Among States.....83
5.16 State Set Trimmer Flow Diagram.....85
5.17 "Test and Trim Events" Flow Diagram.....86
5.18 A More E...