Decomposability - 1st Edition - ISBN: 9780121937508, 9781483217581


1st Edition

Queueing and Computer System Applications

Authors: P. J. Courtois
Editors: Robert L. Ashenhurst
eBook ISBN: 9781483217581
Imprint: Academic Press
Published Date: 28th April 1977
Page Count: 216
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Decomposability: Queueing and Computer System Applications presents a set of powerful methods for systems analysis. This 10-chapter text covers the theory of nearly completely decomposable systems upon which specific analytic methods are based.

The first chapters deal with some of the basic elements of a theory of nearly completely decomposable stochastic matrices, including the Simon-Ando theorems and the perturbation theory. The succeeding chapters are devoted to the analysis of stochastic queuing networks that appear as a type of key model. These chapters also discuss congestion problems in information processing systems, which could be studied by the queuing network models. A method of analysis by decomposition and aggregation for these models is proposed. Other chapters highlight the problem of computer system performance evaluation, specifically the analysis of hardware and software of the dynamic behavior of computer systems and user programs. These topics are followed by a description of an aggregative model of a typical multiprogramming time-sharing computer system. The last chapter examines the existing affinity between the concept of aggregate in nearly completely decomposable structures and the notions of module and level of abstraction so frequently invoked in computer system design and software engineering.

This book will prove useful to both hardware and software designers and engineers, as well as scientists who are investigating complex systems.

Table of Contents




Introduction and Overview

Near-Complete Decomposability

Queueing Networks

Computer System Models

Chapter I Nearly Completely Decomposable Systems

1.1 Eigencharacteristics and Condition Numbers

1.2 The Simon-Ando Theorems

1.3 Interpretation of Theorems

1.4 Aggregation of Variables

1.5 Multilevel Decomposability

1.6 Block Triangular Systems

Chapter II On the Degree of Approximation

2.1 Error Analysis

2.2 Conditioning and Indecomposability of Aggregates

2.3 Block Stochastic Systems

2.4 Error Estimation

2.5 Multilevel Aggregation

2.6 A Posteriori Error Bound

2.7 Conclusions

Chapter III Criterion for Near-Complete Decomposability Equivalence Classes of Aggregates

3.1 Necessary Conditions

3.2 Criterion for Near-Complete Decomposability

3.3 Lumping States

3.4 Classes of Equivalence for Aggregates

Chapter IV Decomposability of Queueing Networks

4.1 Basic Model

4.2 Conditions for Near-Complete Decomposability

4.3 Sufficient Conditions of Network Decomposability

4.4 Discussion

4.5 Central-Server Model

Chapter V Hierarchy of Aggregate Resources

5.1 Decomposition Into Levels of Aggregation

5.2 Level Analysis

5.3 Interlevel Relationship

5.4 Conclusions

Chapter VI Queueing-Network Analysis

6.1 State Dependency

6.2 Arbitrary Service Time Distributions

6.3 Further Generalizations

6.4 Computational Efficiency

Chapter VII Memory Hierarchies

7.1 Basic Assumptions

7.2 Access Probabilities

7.3 Single-Process Storage Hierarchy

7.4 Multiprocess Storage Hierarchy

7.5 Near-Complete Decomposability

7.6 Memory Level Aggregation

7.7 Dynamic Space Sharing

7.8 Linear Storage Hierarchies

Chapter VIII Near-Complete Decomposability in Program Behavior

8.1 Preliminaries

8.2 Existing Models of Program Paging Behavior

8.3 Nearly Completely Decomposable Model of Program Behavior

8.4 Page Fault Rate

8.5 Numerical Example

8.6 Working-Set Size Distribution

8.7 Not Strictly Disjoint Localities

8.8 Conclusion

Chapter IX Instabilities and Saturation in Multiprogramming Systems

9.1 System Model

9.2 User Program Model

9.3 Simplifying Assumptions

9.4 Numerical Data

9.5 Page Fault Rate

9.6 Parachor and Parachron

9.7 Page Transfer Rate

9.8 Decomposability of the Model

9.9 Aggregate Short-Term Equilibrium

9.10 System Long-Term Equilibrium

9.11 Instabilities

9.12 Asymptotic Behavior of the Congestion

9.13 Saturation

9.14 System Response Time

9.15 Conclusions and Open Questions

Chapter X Hierarchical System Design

10.1 Levels of Abstraction

10.2 Aggregation and Ordering of Abstractions

10.3 Aggregation and Stepwise Design Evaluation


Appendix I Proof of Theorem 2.1

Appendix II Proof of Theorem 2.2

Appendix III Numerical Example

Appendix IV Eigenvalues of the Matrix Q(N, 1)




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© Academic Press 1977
Academic Press
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About the Author

P. J. Courtois

About the Editor

Robert L. Ashenhurst

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