Yu-Chi Ho, Xi-Ren Cao

Perturbation Analysis of Discrete Event Dynamic Systems

• Gebundenes Buch

Produktbeschreibung

Dynamic Systems (DEDS) are almost endless: military C31 Ilogistic systems, the emergency ward of a metropolitan hospital, back offices of large insurance and brokerage fums, service and spare part operations of multinational fums . . . . the point is the pervasive nature of such systems in the daily life of human beings. Yet DEDS is a relatively new phenomenon in dynamic systems studies. From the days of Galileo to Newton to quantum mechanics and cosmology of the present, dynamic systems in nature are primarily differential equations based and time driven. A large literature and endless success stories have been built up on such Continuous Variable Dynamic Systems (CVDS). It is, however, equally clear that DEDS are fundamentally different from CVDS. They are event driven, asynchronous, mostly man-made and only became significant during the past generation. Increasingly, however, it can be argued that in the modem world our lives are being impacted by and dependent upon the efficient operations of such DEDS. Yet compared to the successful paradigm of differential equations for CVDS the mathematical modelling of DEDS is in its infancy. Nor are there as many successful and established techniques for their analysis and synthesis. The purpose of this series is to promote the study and understanding of the modelling, analysis, control, and management of DEDS. The idea of the series came from editing a special issue of the Proceedings of IEEE on DEOS during 1988.

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Produktdetails

• The Springer International Series in Engineering and Computer Science 145
• Verlag: Springer / Springer US / Springer, Berlin
• Artikelnr. des Verlages: 978-0-7923-9174-6
• 1991.
• Seitenzahl: 460
• Erscheinungstermin: 30. Juni 1991
• Englisch
• Abmessung: 241mm x 160mm x 31mm
• Gewicht: 830g
• ISBN-13: 9780792391746
• ISBN-10: 0792391748
• Artikelnr.: 22830085

Inhaltsangabe

1. Introduction to Discrete Event Dynamic Systems.- 1.1 Introduction.- 1.2 Models of DEDS.- 2. Introduction to Perturbation Analysis.- 2.1 Notations.- 2.2 A Short History of the Perturbation Analysis Development.- 3. Informal Treatment of the Infinitesimal Perturbation Analysis (IPA) 2.- 3.1 The Basic Idea.- 3.2 Single Class Queueing Networks.- 3.3 A GSMP Formalism for IPA.- 3.4 Realization Ratios.- 3.5 The GI/G/1 Queue.- 3.6 Load Dependent Server and IPA.- 3.7 Remarks about PA.- 4. Foundation of Infinitesimal Perturbation Analysis.- 4.1 Sample Derivative and Interchangeability.- 4.2 Perturbation Analysis for Closed Jackson Network.- 4.3 Realization and Sensitivity Analysis.- 4.4 Sensitivity Analysis of Networks with General Service Distributions.- 4.5 IPA Estimates of the M/G/1 and GI/G/1 Queue.- 4.6 Some Technical Proofs.- 5. Extensions of IPA.- 5.1 System Representation and PA.- 5.2 Another Sufficient Condition for Interchangeability.- 5.3 Routing Probability Sensitivity.- 5.4 The Multiclass M/G/1 Queue and Networks.- 5.5 Smoothed Perturbation Analysis (SPA).- 6. Finite Perturbation Analysis.- 6.1 The Idea of "Cut-and-Paste".- 6.2 The State Matching vs. Event Matching Algorithms.- 6.3 "Cut-and-Paste" as a Generalization of the Rejection Method.- 6.4 First Order Propagation Rules and Approximate EPA.- 7. General Sensitivity Analysis.- 7.1 Efficient Sample Path Generation.- 7.2 Trajectory Projection and State Augmentation.- 7.3 The Likelihood Ratio Approach.- 8. Aggregation, Decomposition, and Equivalence.- 8.1 Equivalent Server and Aggregation.- 8.2 Perturbation Analysis on Aggregated Systems and Aggregated PA.- 8.3 Aggregation and Decomposition of Markov Chains.- 8.4 Decomposition via the A-Segment Algorithm for very Large Markov Chains.- Appendix A. Elementsof Queueing Theory.- Appendix B. elements of Discrete Event Simulation.- Appendix C. Elements of Optimization and Control Theory 3.- Appendix D. A Simple Illustrative Example of the Different Models of DEDS.- Appendix E. A Sample Program of Perturbation Analysis.- References.

Rezensionen

' The book is strongly recommended for graduate students who have had courses in linear algebra, multivariate calculus and a first course in probability theory and stochastic process; as also for practitioners of operations research, engineering and applied mathematicians. ' Indian Journal of Technology October 1992

' The book is strongly recommended for graduate students who have had courses in linear algebra, multivariate calculus and a first course in probability theory and stochastic process; as also for practitioners of operations research, engineering and applied mathematicians. ' Indian Journal of Technology October 1992