/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

/pdf/the-theory-of-industrial-organization-19bejph0ej.pdf

The Theory of Industrial Organization

Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

Fundamentals of Queueing Networks

Preface.- 1. Birth-Death Queues.- 2. Jackson Networks.- 3. Stochastic Comparisons.- 4. Kelly Networks.- 5. Technical Desiderata.- 6. Single-Station Queues.- 7. Generalized Jackson Networks.- 8. A Two-Station Multi-Class Network.- 9. Feedforward Networks.- 10. Brownian Approximations.- 11. Conservation Laws.- 12. Scheduling of Fluid Networks.- Index.

/pdf/fundamentals-of-queueing-networks-performance-asymptotics-3v4585kegn.pdf

Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization

This paper examines the inventories of publicly traded American manufacturing companies between 1981 and 2000. The median of inventory holding periods were reduced from 96 days to 81 days. The average rate of inventory reduction is about 2% per year. The greatest reduction was found for work-in-process inventory, which declined by about 6% per year. Finished-goods inventories did not decline. Firms with abnormally high inventories have abnormally poor long-term stock returns. Firms with slightly lower than average inventories have good stock returns, but firms with the lowest inventories have only ordinary returns.

What Actually Happened to the Inventories of American Companies Between 1981 and 2000

We conduct bottleneck analysis of a deterministic dynamic discrete-flow network. The analysis presupposes only the existence of long-run averages, and is based on a continuous fluid approximation to the network in terms of these averages. The results provide functional strong laws-of-large-numbers for stochastic Jackson queueing networks since they apply to their sample paths with probability one.

https://www.jstor.org/stable/pdfplus/3689886.pdf

Discrete flow networks: bottleneck analysis and fluid approximations

This paper studies the fluid approximation (also known as the functional strong law of large numbers) and the stability (positive Harris recurrence) for a multiclass queueing network. Both of these are related to the stabilities of a linear fluid model, constructed from the first-order parameters (i.e., long-run average arrivals, services and routings) of the queueing network. It is proved that the fluid approximation for the queueing network exists if the corresponding linear fluid model is weakly stable, and that the queueing network is stable if the corresponding linear fluid model is (strongly) stable. Sufficient conditions are found for the stabilities of a linear fluid model.

/pdf/fluid-approximations-and-stability-of-multiclass-queueing-3303tidrsv.pdf

Hong Chen

Papers

Fundamentals of Queueing Networks

Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization

What Actually Happened to the Inventories of American Companies Between 1981 and 2000

Discrete flow networks: bottleneck analysis and fluid approximations

Fluid Approximations and Stability of Multiclass Queueing Networks: Work-Conserving Disciplines